# Hypothesis Testing Problems

1. Consider the hypothesis test given by

ho: m=50

h1: m=>50.

in a random sample of 100 subjects, the sample mean is found to be xbar = 53.4. also the population standard deviation is sigma= 8

Determine the p-value for this test. is there sufficient evidence to justify the rejection of ho? explain.

2) We perform the following hypothesis test of proportion of successes in a population.

Ho: p= 0.7 vs. H1: p< 0.7.
in a sample of 100 items, we discover 63 successes.
what is the conclusion at the a= 0.05 level? explain your answer

3) Given in a sample size of 18, with sample mean 660.3 standard deviation 95.9, we perform the following hypothesis test.

Ho:m=700
H1:m is not equal to =700
what is the conclusion of the test at the a= 0.05 level? explain your answer.

# Hypothesis testing problems

Question #1 / 9
The mean SAT score in mathematics is . The founders of a nationwide SAT preparation course claim that graduates of the course score higher, on average, than the national mean. Suppose that the founders of the course want to carry out a hypothesis test to see if their claim has merit. State the null hypothesis and the alternative hypothesis that they would use.
1 H o:
2 H 1:

Question #2 / 9
The breaking strengths of cables produced by a certain manufacturer have a mean, , of pounds, and a standard deviation of pounds. It is claimed that an improvement in the manufacturing process has increased the mean breaking strength. To evaluate this claim, newly manufactured cables are randomly chosen and tested, and their mean breaking strength is found to be pounds. Can we support, at the level of significance, the claim that the mean breaking strength has increased? (Assume that the standard deviation has not changed.)
Perform a one-tailed test. Then fill in the table below.
Carry your intermediate computations to at least three decimal places, and round your responses as specified in the table. (If necessary, consult a list of formulas.)
1 the null hypothesis H o:
2 the alternative hypothesis H 1:
3 the type of test statistic: Z t chi-square F
4 the value of the test statistic: (Round to at least three decimal places).
5 The critical value at the 0.01 level of significance: (Round to at least three decimal places).
6 Can we support the claim that the mean breaking strength has increased? Yes No

Question #3 / 9
Heights were measured for a random sample of plants grown while being treated with a particular nutrient. The sample mean and sample standard deviation of those height measurements were centimeters and centimeters, respectively.
Assume that the population of heights of treated plants is normally distributed with mean . Based on the sample, can it be concluded that is different from centimeters? Use the level of significance.
Perform a two-tailed test. Then fill in the table below.
Carry your intermediate computations to at least three decimal places and round your answers as specified in the table. (If necessary, consult a list of formulas.)
1 the null hypothesis H o:
2 the alternative hypothesis H 1:
3 the type of test statistic: Z t chi-square F
4 the value of the test statistic: (Round to at least three decimal places).
5 The p-value: (Round to at least three decimal places).
6 At the 0.05 level of significance, can it be concluded that the population mean height of treated plants is different from 36 centimeters? Yes No

Question #4 / 9
A manager at LLD Records is investigating the company’s market research techniques. She learns that much of the market research of college students is done during promotions on college campuses. She also learns that there are other methods of performing market research (for instance, over the phone, in a mall, etc.). In all cases, for each new CD thta LLD Records releases, the company solicits an “intent-to-purchase” score from the student, with being the lowest score (“no intent to purchase”) and being the highest score (“full intent to purchase”).
The manager finds some information on a soon-to-be-released CD. The information details the intent-to-purchase scores from each of several groups of college students, with each group being questioned via a different method. Based on this information, the manager is able to perform a one-way, independent-samples ANOVA test of the hypothesis that the mean intent-to-purchase score for this CD is the same no matter the method of score collection. This test is summarized in the ANOVA table below.
Fill in the missing entry in the ANOVA table (round your answer to at least two decimal places), and then answer the questions below.

Source of variation Degrees of freedom Sum of squares Mean Square F statistic
1 Treatments (Between Groups) 2 290.7 145.4 &#61603;
Error (Within Groups) 72 6540 90.8
Total 74 6830.7

1 How many intent-to purchase scores were examined in all? &#61603;
2 For the ANOVA test, it is assumed that the population variances of intent-to-purchase scores are the same no matter the method of score collection. What is an unbiased estimate of this common population variance based on the sample variances? &#61603;
3 Using the 0.10 level of significance, what is the critical value of the F statistic for the ANOVA test? Round your answer to at least two decimal places. &#61603;
4 Based on this ANOVA, can we conclude that there are differences in the mean intent-to-purchase scores (for this CD) among the different methods of collection? Use the 0.10 level of significance. Yes No

Question #5 / 9
Cris Turlock owns and manages a small business in San Francisco, California. The business provides breakfast and brunch food, via carts parked along sidewalks, to people in the business district of the city.
Being an experienced businessperson, Cris provides incentives for the four salespeople operating the food carts. This year, she plans to offer monetary bonuses to her salespeople based on their individual mean daily sales. Below is a chart giving a summary of the information that Cris has to work with. (In the chart, a “sample” is a collection of daily sales figures, in dollars, from this past year for a particular salesperson.)
Groups Sample Size Sample Mean Sample Variance
Salesperson 1 132 218.8 2461.9
Salesperson 2 92 222.3 1899.5
Salesperson 3 116 209.4 3017.9
Salesperson 4 129 212.2 2515.7

Cris’ first step is to decide if there are any significant differences in the mean daily sales of her salespeople. (If there are no significant differences, she’ll split the bonus equally among the four of them.) To make this decision, Cris will do a one-way, independent-samples ANOVA test of equality of the population means, which uses the statistic

Variation between the samples .

Variation within the samples
For these samples, .

1 Give the numerator degrees of freedom of this F statistic
2 Give the denominator degrees of freedom of this F statistics
3 Can we conclude, using the 0.05 level of significance, that at least one of the salespeople’s mean daily sales is significantly different from that of the others? Yes No

Question #6 / 9
At LLD Records, some of the market research of college students is done during promotions on college campuses, while other market research of college students is done through anonymous mail, phone, internet, and record store questionnaires. In all cases, for each new CD the company solicits an “intent-to-purchase” score from the student, with being the lowest score (“no intent to purchase”) and being the highest score (“full intent to purchase”).
The manager finds the following information for intent-to-purchase scores for a soon-to-be-released CD:
Groups Sample Size Sample Mean Sample Variance
On Campus 25 64.4 127.2
By mail 25 68.7 96.5
By phone 25 62.9 40.5
By internet 25 67.0 98.4
In a store 25 62.8 219.6
The manager’s next step is to conduct a one-way, independent-samples ANOVA test to decide if there is a difference in the mean intent-to-purchase score for this CD depending on the method of collecting the scores.
Answer the following, carrying your intermediate computations to at least three decimal places and rounding your responses to at least one decimal place.

1 What is the value of the mean square for error (the “within groups” mean square) that would be reported in the ANOVA test?
2 What is the value of the mean square for treatments (the”between groups” mean square) that would be reported in the ANOVA test?

Question #7 / 9
The Ellington Dukes are a minor-league baseball team in Ellington, Georgia. As with most other minor-league teams, the Dukes rely heavily on promotions to bring fans to the ballpark. These promotions are typically aimed at fans of specific ages. The management for the Dukes has planned its current promotional schedule according to the following estimates: of fans attending Dukes games are ages to , are ages to , are ages to , are ages to , and are over .
A statistical consulting firm for the Dukes surveyed a random sample of fans attending Dukes games in order to see if these estimates are accurate. The observed frequencies in the sample of for each of the age categories are given in the top row of numbers in Table 1 below. The second row of numbers contains the frequencies expected for a random sample of fans if the Dukes’ management’s estimates are accurate. The bottom row of numbers in Table 1 contains the values

= (Observed frequency – Expected frequency)2

Expected frequency
for each of the age categories.
Fill in the missing values of Table 1. Then, using the level of significance, perform a test of the hypothesis that the management’s estimates are accurate. Then complete Table 2.
Round your responses for the expected frequencies in Table 1 to at least two decimal places. Round your responses in Table 1 to at least three decimal places. Round your responses in Table 2 as specified.
Table 1: Information about the Sample

Age Group
0 to 12 13 to 18 19 to 35 36 to 55 Over 55
Observed freq 35 23 51 39 32
1 Expected freq 18 45 36
2
1.389 0.8 0.444

Table 2: Summary of the Hypothesis Test

1 the type of test statistic: Z t chi-square F
2 the value of the test statistic:
(Round the answer to at least two decimal places).
3 The critical value for a test at the 0.10 level of significance: (Round your answer to at least two decimal places).
4 Can we conclude that the management’s original estimates for the age distribution of fans attending Dukes games are inaccurate? Use the 0.10 level of significance. Yes No

# Hypothesis testing problems

13. For each of the following:
(a) State which two populations are being compared

(b) State the research hypothesis
(c) State the null hypothesis
(d) Say whether you should use a one-tailed or two-tailed test and why.

i. In an experiment, people are told to solve a problem by focusing on the details.
Is the speed of solving the problem different for people who get such instructions compared to the speed for people who are given no special instructions?

ii. Based on anthropological reports in which the status of women is scored on a
10-point scale, the mean and standard deviation across many cultures are known. A new culture is found in which there is an unusual family arrangement.
The status of women is also rated in this culture. Do cultures with the unusual family arrangement provide higher status to women than cultures in general?

iii. Do people who live in big cities develop more stress-related conditions than people in general?

16. A researcher wants to test whether a certain sound will make rats do worse on learning tasks. It is known that an ordinary rat can learn to run a particular maze correctly in 18 trials, with a standard deviation of 6. (The number of trials to learn this maze is normally distributed.) The researcher now tries an ordinary rat in the maze, but with the sound. The rat takes 38 trials to learn the maze.

(a) Using the .05 level, what should the researcher conclude?
Solve this problem explicitly using all five steps of hypothesis testing, and illustrate your answer with a sketch showing the comparison distribution, the cutoff (or cutoffs), and the score of the sample on this distribution.

(b) Then explain your answer to someone who has never had a course in statistics (but who is familiar with mean, standard deviation, and Z scores).

20. In an article about anti-tobacco campaigns, Siegel and Biener (1997) discuss the results of a survey of tobacco usage and attitudes, conducted in Massachusetts in 1993 and 1995; Table 4-4 shows the results of this survey. Focusing on just the first line (the percentage smoking 25 cigarettes daily), explain what this result means to a person who has never had a course in statistics. (Focus on the meaning of this result in terms of the general logic of hypothesis testing and statistical significance.)

Table 4-4 Selected Indicators of Change in Tobacco Use, ETS Exposure, and Public Attitudes toward Tobacco Control Policies-Massachusetts, 1993-1995
1993 1995
Percentage smoking >25 cigarettes daily 24 10*

Percentage smoking <15 cigarettes daily 31 49*

Percentage smoking within 30 minutes of waking 54 41

Environmental Tobacco Smoke Exposure

Percentage of workers reporting a smoke free worksite 53 65*

Mean hours of ETS exposure at work during prior week 4.2 2.3*

Percentage of homes in which smoking is banned 41 51*

Attitudes Toward Tobacco Control Policies

Percentage supporting further increase in tax on
tobacco with funds earmarked for tobacco control 78 81

Percentage believing ETS is harmful 90 84

Percentage supporting ban on vending machines 54 64*

Percentage supporting ban on support of sports and cultural
events by tobacco companies 59

# Hypothesis testing problems

1. A study has been carried out to compare the United
Way contributions made by clerical workers from three
local corporations. A sample of clerical workers has been
randomly selected from each firm, and the dollar amounts
of their contributions are as follows. (Use data file XR12027.)

Firm 1 Firm 2 Firm 3
199 108 162
236 104 86
167 153 160
263 218 135
254 210 207
96 201

a. What are the null and alternative hypotheses for
this test?

b. Use ANOVA and the 0.05 level of significance in
testing the null hypothesis identified in part (a).

2. For the following summary table for a one-way
ANOVA, fill in the missing items (indicated by asterisks),
identify the null and alternative hypotheses, then use the
0.025 level of significance in reaching a conclusion
regarding the null hypothesis.

Variation Sum of Degrees of Mean
Source Squares Freedom Square F

Treatments 665.0 4 *** ***
Error *** 60 ***

Total 3736.3 ***

3. From the one-day work absences during the past year, the
personnel director for a large firm has identified the day of the
week for a random sample of 150 of the absences.
Given the following observed frequencies, and for
a = 0.01, can the director conclude that one-day absences
during the various days of the week are not equally likely?
Monday Tuesday Wednesday Thursday Friday

42 18 24 27 39 150

4. The outstanding balances for 500 credit-card
customers are listed in file XR13026. Using the 0.10 level of
significance, examine whether the data could have come
from a normal distribution.

Balance
3917
3968
3176
3318
4282
3666
2585
3831
3684
4213
3857
3142
2876
3925
3131
3409
3288
3221
4050
3248
2743
3613
3094
3599
3215
2818
3417
3514
3330
3623
3769
3860
3897
3514
4121
3378
3846
3401
3186
2813
3268
3762
3492
4095
4165
4252
3547
3483
3840
3691
3877
3584
3349
3541
4014
3475
2962
3618
2945
3917
2955
3119
3181
2921
4057
3379
3453
3736
3622
3338
3697
3771
3623
3512
3704
3696
3490
3722
3570
2987
3032
3813
3685
3361
3633
3472
3449
4008
3595
4263
2993
3337
2953
3742
3671
3942
3480
3576
3009
3834
3932
3383
3426
3157
3024
3444
3221
3924
3330
3391
3024
2973
3322
3472
3704
2946
3802
4397
3644
3839
3754
3503
2983
3662
3881
2836
3490
3444
3845
3544
3748
3288
3332
3497
2803
3975
2959
3318
4093
3673
3132
3516
3564
3765
3571
3848
3450
3264
4047
3503
3142
3614
3002
3110
3318
4087
3817
3719
3941
3701
3508
3262
3207
3319
4023
3451
3319
3403
3352
3416
3189
3246
3423
3742
3715
3692
3865
3878
3880
3497
3571
3465
2848
4360
3243
3402
2980
3592
3278
3875
2991
3266
3307
4191
3466
3525
3683
3601
3840
3837
3575
3702
3451
3980
4082
3472
3913
3036
3640
3202
3891
3875
3397
3716
3367
3206
3535
2926
3265
4084
3537
3382
3965
4083
3717
3048
3832
3476
3519
2870
3407
3422
3622
3281
3925
3456
3863
3776
3440
3615
3297
3452
3301
4036
3366
3827
3076
3458
3670
3388
3757
3103
4552
3804
3492
3682
3088
3099
4167
3864
3840
3569
3667
3158
3354
3351
3881
3383
2614
3244
3603
3210
2908
3560
3331
3064
3529
3352
3995
3341
3300
4334
3812
4181
3019
4163
3931
3872
3816
3730
3789
3427
2843
3204
3170
3284
3557
3427
3438
3689
4106
3036
3366
3879
3757
2993
3894
3879
4109
3536
3174
3900
3690
3157
3417
3193
3484
4389
3679
3500
3155
4167
4107
3556
3156
3821
3761
3804
3752
3638
3016
3369
2953
3547
3689
3520
3685
3253
3468
3420
3455
4155
3846
3766
3425
4182
3378
3154
3605
3735
4145
3459
3848
3137
4435
3156
3184
3738
3214
3933
3790
3677
3942
3407
3413
3391
3451
3581
3411
3409
3658
3462
3278
3783
3712
4104
3764
3920
3218
3272
3725
4054
3448
3139
3905
2862
3527
3363
3562
3593
3689
3132
3703
3922
3230
3995
3538
3451
3365
3062
3153
3618
3482
3114
3902
3763
3566
3210
3615
3264
3117
3338
3276
3353
3534
3868
3785
3700
3760
3541
3644
2903
2975
3184
3520
4044
3470
3357
3596
3094
3225
3333
3383
3877
3423
3482
3784
4086
4367
3592
3262
3755
3396
3361
3900
3459
3791
3891
3961
3184
3998
3534
3758
3375
3399
3262
4095
3544
3989
3716
3101
3458
2626
4196
3707
3766
3368
3767
3092
4269
3357
3520
3852
3137
3401
3703
3792
3458
3322
3479
2871
3777
3327
3698
3443
3927
3605
3692
3568
3733
3281
3362
3549
3684
3480
3306
3573
3187
3068
2750

5. The following data represent x = boat sales and
y = boat trailer sales from 1995 through 2000.

Boat Sales Boat Trailer Sales
Year (Thousands) (Thousands)

1995 649 207
1996 619 194
1997 596 181
1998 576 174
1999 585 168
2000 574 159

a. Determine the least-squares regression line and interpret
its slope.

b. Estimate, for a year during which 500,000 boats are
sold, the number of boat trailers that would be sold.

c. What reasons might explain why the number of boat
trailers sold per year is less than the number of
boats sold per year?

6. For each of 10 popular prescription drugs, file
XR15042 lists the retail price (in U.S. dollars) for the drug
in several different countries, including the United States,
Canada, Great Britain, and Australia. Determine and
interpret the coefficients of correlation and
determination for U.S. prices versus Canadian prices.

Drug US Price Canada Price Great Britain Price Australia Price
Prilosec 3.31 1.47 1.67 1.29
Prozac 2.27 1.07 1.08 0.82
Lipitor 2.54 1.34 1.67 1.32
Prevacid 3.13 1.34 0.82 0.83
Epogen 23.40 21.44 27.48 29.24
Zocor 3.16 1.47 1.73 1.75
Zoloft 1.98 1.07 0.95 0.84
Zyprexa 5.27 3.39 2.86 2.63
Claritin 1.96 1.11 0.41 0.48
Paxil 2.22 1.13 1.70 0.82

# Hypothesis testing problems.

1.

Ms. Lisa Monnin is the budget director for Nexus Media, Inc. She would like to compare the daily travel expenses for the sales staff and the audit staff. She collected the following sample information.

Sales (\$) 131 135 146 165 136 142
Audit (\$) 130 102 129 143 149 120 139

At the .10 significance level, can she conclude that the mean daily expenses are greater for the sales staff than the audit staff? What is the p-value?

2.

The management of Discount Furniture, a chain of discount furniture stores in the Northeast, designed an incentive plan for salespeople. To evaluate this innovative plan, 12 salespeople were selected at random, and their weekly incomes before and after the plan were recorded.

Salesperson Before After
Sid Mahone \$320 \$340
Carol Quick 290 285
Tom Jackson 421 475
Andy Jones 510 510
Jean Sloan 210 210
Jack Walker 402 500
Peg Mancuso 625 631
Anita Loma 560 560
John Cuso 360 365
Carl Utz 431 431
A. S. Kushner 506 525
Fern Lawton 505 619

Was there a significant increase in the typical salesperson’s weekly income due to the innovative incentive plan? Use the .05 significance level. Estimate the p-value, and interpret it.

3.

A recent study focused on the number of times men and women who live alone buy take-out dinner in a month. The information is summarized below.

Statistic Men Women
Mean 24.51 22.69
Standard deviation 4.48 3.86
Sample size 35 40

At the .01 significance level, is there a difference in the mean number of times men and women order takeout dinners in a month? What is the p-value?

4.

The manager of a computer software company wishes to study the number of hours senior executives spend at their desktop computers by type of industry. The manager selected a sample of five executives from each of three industries. At the .05 significance level, can she conclude there is a difference in the mean number of hours spent per week by industry?

Banking Retail Insurance
12 8 10
10 8 8
10 6 6
12 8 8
10 10 10

# Hypothesis testing problems

1. Although many people think they can put a meal on the table in a short period of time, an article reported that they end up spending about 40 minutes doing so. Suppose another study is conducted to test the validity of this statement. A sample of 25 people is selected, and the length of time to prepare and cook dinner (in minutes) is recorded, with the following results-see attached file called DINNER.

a.) Is there evidence that the population mean time to prepare and cook dinner is different from 40 minutes? Use the p-value approach and a level of significance of 0.05.

b.) What assumption about the population distribution is needed in order to conduct the t test in (a)?

2. Nondestructive evaluation is a method that is used to describe the properties of components or materials without causing any permanent physical change to the units. It includes the determination of properties of materials and the classification of flaws by size, shape, type, and location. This method is most effective for detecting surface flaws and characterizing surface properties of electrically conductive materials. Data were collected that classified each component as having a flaw or not, based on manual inspection and operator judgement, and the data also reported the size of the crack in the material. Do the components classified as unflawed have a smaller mean crack size than components classified as flawed? The results in terms of crack size (in inches) are in the attachment: CRACK.

a.) Assuming that the population variances are equal, is there evidence that the mean crack size is smaller for the flawed specimens than for the flawed specimens? (Use ? = 0.05).

# Hypothesis testing problems

There are 4 questions in word file and 1 question in excel file.

Thanks

5. The manufacturer of the X-15 steel-belted radial truck tire claims that the mean mileage the tire can be driven before the tread wears out is 60,000 miles. The standard deviation of the mileage is 5,000 miles. The Crosset Truck Company bought 48 tires and found the mean mileage for their trucks is 59,5000 miles. Is Crosset&#8217;s experience different from that claimed by the manufacturer at the .05 significance level?

12. A recent article in USA Today reported that a job awaits only one in three new college graduates. The major reasons given were an overabundance of college graduates and a weak economy. A survey of 200 recent graduates from your school revealed that 80 students had jobs. At the .02 significance level, can we conclude that a larger proportion of students at your school have jobs?

17. The Rocky Mountain district sales manager of Rath Publishing, Inc., a college textbook publishing company, claims that the sales representatives make an average of 40 sales calls per week on professors. Several reps say that this estimate is too low. To investigate, a random sample of 28 sales representatives reveals that the mean number of call made last week was 42. The standard deviation of the sample is 2.1 calls. Using the .05 significance level, can we conclude that the mean number of calls per salesperson per week is more than 40?

40. From past experience a television manufacturer found that 10 percent or less of its sets needed any type of repair in the first two years of operation. In a sample of 50 sets manufactured two years ago, 9 needed repairs. At the .05 significance level, has the percent of sets needing repair increased? Determine the p-value.

# Hypothesis testing problems

9.69 Late payment of medical claims can add to the cost of health care. An article (M. Freudenheim, “The Check in Not in the Mail,” The New York Times, May 25, 2006, pp.C1, C6) reported that for one insurance company, 85.1% of the claims were paid in full when first submitted. Supposed the insurance company developed a new payment system in an effort to increase this percentage. A sample of 200 claims processed under this system revealed that 180 of the claims were paid in full when first submitted.

a. At the 0.05 level of significance, is there evidence that the proportion of claims processed under this new system is higher than the article reported for the previous system?
b. Compute the p-value and interpret its meaning.

9.70 The high cost of gasoline in the spring of 2006 had many people reconsidering their summer vacation plans. A survey of 464 Cincinnati-area adults found that 55 said they were planning on modifying or canceling their summer travel plans because of high gas prices (“Will You Travel?” The Cincinnati Enquirer, May 3, 2006, p.A10.)

a. Use the six-step critical value approach to hypothesis testing and a 0.05 level of significance to try to prove that the majority of Cincinnati-area adults were planning on modifying or canceling their summer travel plans because of high gas prices.
b. Use the five-step p- value approach to hypothesis testing and a 0.05 level of significance to try to prove that the majority of Cincinnati-area adults were planning on modifying or canceling their summer travel plans because of high gas prices.
c. Compare the results of (a) and (b).

9.72 A Wall Street Journal poll (“What’s News Online,” The Wall Street Journal, March 30, 2004, p.D7) asked respondents if they trusted energy-efficiency ratings on cars and appliances; 552 responded yes, and 531 responded no.

a. At the 0.05 level of significance, use the six-step critical the percentage of people who trust energy-efficiency rating differs from 50%.
b. Use the five-step p-value approach. Interpret the meaning of the p-value.

# Hypothesis Testing Problems,

Example 1: Suppose data on retail prices of a cholesterol reducing drug were collected from randomly selected Pharmacies of two states (16 pharmacies from State1 and 13 from State 2) with the following values:
State 1 State2
125.05 145.32
137.56 131.19
142.5 151.65
145.95 141.55
117.49 125.99
142.75 126.29
121.99 139.19
117.49 156
141.64 137.56
128.69 154.1
130.29 126.41
142.39 114
121.99 144.99
141.3
153.43
133.39
Given the two samples can we conclude that the average retail prices do not significantly differ by State? Give conclusion for two cases (a) population variances are equal; and (b) population variances are unequal.
Solve this problem using calculator, with formulas and the t-table. Work with t-values only.

Example 2: A study was conducted to determine if there was a difference in humor content in British and American trade magazine advertisements. An independent random sample of 203 British trade magazines contained 54 humorous ads while the other independent sample of 270 American trade magazine advertisements contained 56 humors. Does this data set provide evidence that there are more frequent humorous content in ads of British compared to American trade magazines?
Work it out with calculator, Z table and the formulas.

Example 4: Test H0: ?1 ? ?2; H1: ?1 > ?2 at ? = .05, when X ?1 = 75.4, X ?2 = 72.2, s1 = 3.3, s2 = 2.1, n1 = 6, n2 = 6. Indicate which test you are performing; show the hypotheses, the test statistic and the critical values and mention whether one-tailed or two-tailed. Please use Excel for calculation.

# Hypothesis testing problems

1) Test equally likeliness of random numbers.
a. Use Excel to generate 500 random digits per the instructions below.

1. Click on fx and from the Math&Trig category, choose RANDBETWEEN and click OK.

2. In the bottom of the dialog box enter 0 and in the top enter, then click OK. This tells Excel to generate digits between 0 and 9.

3. Highlight cells A1 through A500 so you get 500 digits generated.

4. You can record these results in a table such as you did previously for a histogram with the Excel “bin” feature. In column B enter the values 0-9 in
the first 10 rows. How use Histogram in Data Analysis to generate a
frequency table to better see the results.

b. Use a significance level of 0.05 to test the claim that your sample of digits come from a population where all digits are equally likely. Report on whether or not Excel is properly generating random numbers. Make sure to show all our work in the submitted spreadsheet.

2) Test for the same mean. See at the attached Words.xls data file for this part of the project.

a. Test the null hypothesis that the six samples of word counts for males (odd columns ending in M) are from a population with the same mean.

b. Test the null hypothesis that the six samples of word counts for females (even columns) are from a population with the same mean.

c. If we want to compare the number of words spoken by men to the number spoken by women, does it make sense to combine the six columns to word counts for males and the same for females before then comparing?

3) Testing Random Numbers by nonparametic methods.

a. Use the random numbers created in part 1) above and test for randomness using three of the methods in chapter 13. Again, show all work and report on the findings of each.

4) Quality control process testing. Again, use the RANDBETWEEN function in Excel. This time generate 200 random numbers between 1 and 100 and output it to one column. Then do the same for until you have 20 columns of which are 200 in length that all have values between 1 and 100.

a. The above generated data is to simulate 20 days of a quality control process. Consider an outcome of 1-5 to be a defect and an outcome of 6-100 to be an acceptable result. Note that this corresponds to a 5% rate of defects.

b. Construct a p chart for the proportion of defective calculators, and determine whether the process is within statistical control. The process is stable with p = 0.05 so a conclusion that it is not stable would be a type I error which means we would have a false positive signal causing use to think that the process should be adjusted when, in fact, it was fine.

c. Simulate another 10 days of manufacturing calculators (as in part a), but modify these 10 so that the defect rate is 10% instead of 5%.

d. Combine the data from parts a) an c) to represent a total of 30 days of results. Construct a p chart for this combined sample. Is the process out of control or not? If we conclude it is not, we would make a type II error which means that we would believe the process was fine when it should be adjusted to correct the 10% rate of defects.

e. Again, make all your data presentable and report on your findings.

# Hypothesis testing problems

Need help setting up the problem. I understand the mechanics of the problem, I am having trouble setting up P1 and P2 based on the 2 way table (established from the data).

——————————————————————-
A market research consultant hired by the Pepsi-Cola Co is interested in determining whether there is a difference between the portions of female and male consumers who favor Pepsi Cola over Coke Classic in a particular urban location. A random sample of 250 consumers from the market under investigation is provided in the file PepsiCoke.xls

a. Separate the 250 random samples by gender, perform a statistical test to determine if there is a difference at the alpha = .10 level.

b. Marketing managers at the Pepsi-Cola company have asked their market research consultant to explore further the potential differences in the portions of women and men who prefer drinking Pepsi to coke Classic. Specifically, Pepsi managers would like to know whether the potential difference between the portions of female and male consumers who favor Pepsi varies by age of the consumer. As such, assess whether this difference varies across the four given age categories. Employ a 10% significance level.

# Hypothesis testing problems

Please see attached file for full problem description.

1- At LLD Records, some of the market research of college students is done during promotions on college campuses, while other market research of college students is done through anonymous mail, phone, internet, and record store questionnaires. In all cases, for each new CD the company solicits an “intent-to-purchase” score from the student, with being the lowest score (“no intent to purchase”) and being the highest score (“full intent to purchase”).
The manager finds the following information for intent-to-purchase scores for a soon-to-be-released CD
Group Sample size Sample Mean Sample variance
On campus 23 69.3 86.3
By mail 23 63.7 45
By phone 23 58.9 99.8
By internet 23 61.7 41.1
In a store 23 61 106.4

The manager’s next step is to conduct a one-way, independent-samples ANOVA test to decide if there is a difference in the mean intent-to-purchase score for this CD depending on the method of collecting the scores.
Answer the following, carrying your intermediate computations to at least three decimal places and rounding your responses to at least one decimal place.
a- What’s the value of the mean square for error (the “within groups” mean square) that would be reported in the ANOVA test?
b- What’s the value of the mean square for treatment (the “within groups” mean square) that would be reported in the ANOVA test?

2- In an effort to counteract student cheating, the professor of a large class created four versions of a midterm exam, distributing the four versions among the students in the class, so that each version was given to students. After the exam, the professor computed the following information about the scores (the exam was worth points):
Group Sample size Sample Mean Sample variance
Version A 75 159.5 270.3
Version B 75 153 331.6
Version C 75 157.5 365.6
Version D 75 153.7 331.4

The professor is willing to assume that the populations of scores from which the above samples were drawn are approximately normally distributed and that each has the same mean and the same variance.
Answer the following, carrying your intermediate computations to at least three decimal places and rounding your responses to at least one decimal place.
a- give an estimate of this common population variance by pooling the sample variances given.
b- give an estimate of this common population variance by pooling the sample means given.

3- Emma’s On-the-Go, a large convenience store that makes a good deal of money from magazine sales, has three possible locations in the store for its magazine rack: in the front of the store (to attract “impulse buying” by all customers), on the left-hand side of the store (to attract teenagers who are on that side of the store looking at the candy and soda), and in the back of the store (to attract the adults searching through the alcohol cases). The manager at Emma’s experiments over the course of several months by rotating the magazine rack among the three locations, choosing a sample of days at each location. Each day, the manager records the amount of money brought in from the sale of magazines.
Below are the sample mean daily sales (in dollars) for each of the locations, as well as the sample variances:
Group Sample size Sample Mean Sample variance
Front 44 212.1 454.9
Left-hand side 44 219.7 295.4
Right-hand side 44 219 417.1

Suppose that we were to perform a one-way, independent-samples ANOVA test to decide if there is a significant difference in the mean daily sales among the three locations.
Answer the following, carrying your intermediate computations to at least three decimal places and rounding your responses to at least one decimal place.
a- What’s the value of the mean square for error (the “within groups” mean square) that would be reported in the ANOVA test.
b- What’s the value of the mean square for treatment (the “within groups” mean square) that would be reported in the ANOVA test.

# Hypothesis testing problems

Refer to the real estate data which report information on the homes sold in Denver Colorado year at:

http://highered.mcgraw-hill.com/sites/0073030228/student_view0/index.html

.A. At the .05 significance level can we conclude that there is a difference in the mean selling price of the homes with a pool and hoes without a pool?

B. at the .05 significance level can we conclude that thee is a difference in the mean selling price of homes with an attached garage

C, at the .05 significance level can we conclude that there is difference in the mean selling price of homes in township1 and township 2

D. find the median and selling prices of the homes. Divide the homes into two groups those that sold for more or equal to the median and those who sold for less. Is there a difference in the proportion of homes with a pool for those that sold at or above the median price versus those which sold for less than the median price? Use the .05 significance level.

Ques 2:
Refer to the base ball 2005 data at:

http://highered.mcgraw-hill.com/sites/0073030228/student_view0/index.html
which report information on the 30 major baseball teams.

A. at the .05 significance level, can we conclude that there is a difference in the mean salary of teams in the American versus teams in the national league.

B. at the .05 significance level, can we conclude that there is a difference in the mean home attendance of teams in the American league versus teams in the national league.

C. computes the mean and the standard deviation of the number of wins for the 10 items with the highest salaries. Do the same for the 10 teams with the lowest salaries. At the .05 significance level?is there a difference in the mean number of wins for the two groups

# Hypothesis testing problems –

The Rocky Mountain district sales manager of Rath Publishing, Inc., a college textbook publishing company, claims that the sales representatives make an average of 40 sales calls per week on professors. Several reps say that this estimate is too low. To investigate, a random sample of 28 sales representatives reveals that the mean number of calls made last week was 42. The standard deviation of the sample is 2.1 calls. Using the 0.05 significance level, can we conclude that the mean number of calls per salesperson per week is more than 40? (Remember to complete the 5 step hypothesis testing procedure to answer this question).
Can you help me with this in Excel?

H
: m = 40
H
: m > 40
Reject H
if t > 1.703.
t = 42 – 40 5.04
2.1¸Ö28
Reject H
and conclude the mean number is greater than 40.

# Hypothesis testing problems

The manager of a driving school claims that the mean time taken to learn how to drive a car is 8 hours or less for all new drivers. A sample of 16 new drivers showed that the mean time taken by them to learn how to drive the car is 9.5 hours with a standard deviation of 1.5 hours. Test the manager’s claim at the 1% significance level.

# Hypothesis testing problems

Work should be done in EXcel

Refer to the Wage data which report information on the annual wages for a SAMPLE OF 100 WORKERS. ALSO INCLUDED ARE VARIABLES RELATING TO THE INDUSTRY, YEARS OF EDUCATION, AND GENDER FOR EACH OTHER WORKER.(data can be found at

http://highered.mcgraw-hill.com/sites/0073030228/student_view0/index.html

a. Conduct a test of hypothesis to determine if the mean annual wage is greater than \$30, 000. Use the .05 significance level. Determine the p-value and interpret the results.

b. Conduct a test of hypothesis of hypothesis to determine if the mean years of experience is different from 20. Use the .05 significance level. Determine the p-value and interpret the results.

c. Conduct a test of hypothesis to determine the mean age is less than 40. Use the .05 significance level. Determine the p value and interpret the results.

d. Conduct a test of hypothesis to determine if the proportion of Union workers is greater than 15 % Use the .05 level of significance, and report the p value.

# Hypothesis testing problems

All of these questions are for my stat’s class. I am having a really hard time understanding what needs to be done. I really want to learn what is going on.. I have double the amount of homework than the questions below. I went ahead and took one question from each section to get help with so I can see how to get the answers and see if I can work the similar question in my homework by myself. Any help would be greatly appreciated!

# Hypothesis testing problems :

vehicle Miles per gallon xbar variance
Panzer 9.3, 9.3 9.3 8.6 8.7 9.3 9.3 9.91 0.10

T-34 8.7, 7.7, 7.7, 8.7, 8.2, 9.0,7.4,7.0 8.03 0.60

Sherman 7.2,7.9,6.8,7.4,6.5,6.6,6.7,6.5,6.5,7.1,6.7,5.5,7.3 6.82 0.34

you are also given that xbar=7.99

What is the test statistic? use a 5% significance level(95% confidence interval) to test the claim that the different vehicle categories have the same MPG.

# Hypothesis testing problems

I am looking for solutions on the attached questions please.
I would like to have answers and their solutions> like this i can learn to solve them myself.

BUSN 5760 Final Exam Problems: Set up and solve each of the following problems using the Excel files on the course website. Print the output and have it ready BEFORE taking the online Final Exam Part One. Be prepared to answer questions regarding the direction of the hypothesis test, the p-value, the decision to reject or not, and the conclusion. NOTE: You may collaborate on this problem set insofar as the preparation and discussion of the output. Once you open the actual exam, you must work independently. Remember to check your work before proceeding to the exam!

1. [2%] ONE SAMPLE HYPOTHESIS TEST FOR MEAN: A bowler who has averaged 196 pins in the past year is asked to experiment with a ball made of a new kind of material. If he rolls 25 games with the new ball, averaging 204 pins with a standard deviation of 24.9, can one conclude at a level of significance of .01 that the new ball has improved his game?
1a) Direction = UPPER TAILED / LOWER TAILED / 2-TAILED (circle one)
1b) P-value = ________________
1c) REJECT THE NULL or DO NOT REJECT THE NULL? (circle one)
1d) Can we conclude the ball improved his game? YES or NO (circle one)

2. [2%] ONE SAMPLE HYPOTHESIS TEST FOR PROPORTION: The Webster University librarian believes that more than 60% of the books checked out by students was fictional material. In a random sample of 1000 students who checked books out in the last year, 628 checked out fictional material. What can one conclude about the librarian’s hypothesis at a level of significance of .05?
2a) Direction = UPPER TAILED / LOWER TAILED / 2-TAILED (circle one)
2b) P-value = ________________
2c) REJECT THE NULL or DO NOT REJECT THE NULL? (circle one)
2d) Can we conclude the librarian’s claim is correct? YES or NO (circle one)

3. [2%] TWO SAMPLE HYPOTHESIS TEST FOR MEAN – INDEPENDENT SAMPLES: Eight college students were randomly divided into 2 groups of 4 each to test whether background music reduces studying capacity. Each person was tasked with memorizing a list of 20 words. Group 1 had music playing through earphones they were wearing. Group 2 was not distracted. The following are the number of words correctly remembered by each subject. Test whether the music reduces studying capacity at a .05 level of significance.
Group 1 — DISTRACTED Group 2 – NOT DISTRACTED
Sample mean = 7
Sample size = 4
Sample std.dev. = 2.5 Sample mean = 14
Sample size = 4
Sample std.dev. = 3.5

3a) Direction = UPPER TAILED / LOWER TAILED / 2-TAILED (circle one)
3b) P-value = ________________
3c) REJECT THE NULL or DO NOT REJECT THE NULL? (circle one)
3d) Can we conclude that music reduces studying capacity? YES or NO (circle one)

4. [2%] TWO SAMPLE HYPOTHESIS TEST FOR PROPORTION: Before starting his campaign for mayor, Mr. Emory Board decided to do a study to see if there was a difference in the proportion of registered men and women voters who actually vote (so he would know whom to target his campaign toward). Of the 100 men and 150 women surveyed, 50 men and 100 women admitted to voting. What can he conclude at the .05 level of significance?
4a) Direction = UPPER TAILED / LOWER TAILED / 2-TAILED (circle one)
4b) P-value = ________________
4c) REJECT THE NULL or DO NOT REJECT THE NULL? (circle one)
4d) Can we conclude a difference in voting patterns for men vs. women?
YES or NO (circle one)

5. [2%] TWO SAMPLE HYPOTHESIS TEST FOR PAIRED SAMPLES: In a study of the effectiveness of a reducing diet, the following “before and after” figures (in pounds) were obtained for a sample of 4 adult women in their 30’s. What can we conclude from these figures at a level of significance of .01?
Group 1 — BEFORE Group 2 – AFTER
Woman #1
Woman #2
Woman #3
Woman #4 134
147
178
122 130
140
165
122
5a) Direction = UPPER TAILED / LOWER TAILED / 2-TAILED (circle one)
5b) P-value = ________________
5c) REJECT THE NULL or DO NOT REJECT THE NULL? (circle one)
5d) Can we conclude that the diet worked? YES or NO (circle one)

6. [2%] ANOVA: Three groups of 5 students were tested in their ability to correctly answer a 10-question quiz under different formats. Group 1 had a True/False quiz, Group 2 had a Fill-In quiz, and Group 3 had a Multiple Choice quiz. Their scores were as follows:

True/False Fill-In Multiple Choice
6 3 6
8 5 10
9 6 6
7 7 8
10 5 7

Test whether there was a difference in performance on answering the same general questions under different formats. Use a .05 level of significance.

6a) P-value = ________________
6b) REJECT THE NULL or DO NOT REJECT THE NULL? (circle one)
6c) Can we conclude a difference in means? YES or NO (circle one)
6d) If the null is rejected, which specific differences are statistically significant?
T/F vs. Fill-in Fill-in vs. Multiple Choice T/F vs. Multiple Choice
(circle all that apply)

7. [2%] CHI SQUARE TEST OF INDEPENDENCE: Of a sample of 80 single and married women surveyed, we obtained the following data as to the sizes of cars each one owns (assuming 1 car per person). Test whether car size is independent of marital status at the .01 significance level.
Compact Midsize Luxury TOTAL
Single 8 14 8 30
Married 32 10 8 50
TOTAL 40 24 16 80

7a) P-value = ________________
7b) REJECT THE NULL or DO NOT REJECT THE NULL? (circle one)
7c) Can we conclude that car size is dependent on marital status? YES or NO
(circle one)

8. [3%] CORRELATION & REGRESSION: Dr. A. Nova wanted to test his theory that there was a relationship between one’s attendance and one’s performance on his Sadistics exams. He tracked the number of days absent for each of his students this term along with their course averages (shown below). Test whether there is a correlation between the two at a .05 significance level. Also use the regression model to predict a student’s average if he/she misses 4 classes. BE PREPARED TO ANSWER SIX QUESTIONS REGARDING THE OUTPUT.
Days Absent Course Average
Antonio
Bertram
Cecil
Dudley
Eduardo
Fazzio
Guido
Harvey
Ignatius
Jeremiah 3
1
7
5
0
8
5
3
9
2 85
90
63
78
99
65
80
78
47
88

9. [3%] MULTIPLE LINEAR REGRESSION: Dr. A. Nova conducted a survey to see how well the students performed this semester (measured by their GPA) as a function of their age, gender and course load. The following output shows the first run of multiple linear regression. BE PREPARED TO ANSWER SIX QUESTIONS REGARDING THE OUTPUT. (note: for Gender, 0 = Male, 1 = Female).

10. [3%] FORECASTING: The Surgical Intensive Care Unit would like to be better prepared by forecasting the number of surgical patients they should expect. The past 15 days shows the following numbers of surgeries performed. Conduct a 3-period moving average, an exponential smoothing forecasting using an alpha of .25, and a seasonal forecast with 3 seasons.

Day Surgeries
1 10
2 8
3 12
4 10
5 9
6 14
7 11
8 10
9 15
10 13
11 13
12 16
13 14
14 13
15 18

10a) Forecast for day 16 using 3-period Moving Average = ________________
10b) Forecast for day 16 using Exponential Smoothing (alpha = .25) =________
10c) Forecast for day 16 using Seasonality with 3 seasons = _______________

# Hypothesis testing problems

I am trying to understand how to analyze the attached spreadsheet so I can explain to class mates. there are four tabs that I need help on

# Hypothesis testing problems

1. 20 problems
2. If confidence level is not given, assume 95%
3. Please show calculation using formula and using appropriate z table, student’s t table, or Poisson table, etc.

See attached file for full problem description.

# Hypothesis testing problems

1. Sandy’s Pizza has generally assumed that the mean age of its customers was 30 years of age or younger. A random sample of 50 customers revealed the following:

X-bar=30.76 years and s=3.6 years

Does the sample data provide sufficient evidence to conclude that the mean age of Sandy’s customers is greater than 30 years (using alpha=.05)? In answering this question be sure to address all of the points below.
a. State the null and alternative hypothesis

b. State the level of significance

c. Find the critical value (or values) and clearly show the rejection and non-rejection regions

d. Compute the test statistic

e. Decide whether you can reject Ho and Accept Ha or not.

f. Explain and interpret your conclusion in part e.

g. Determine the observed p-value for the hypothesis test and interpret this value. What does this mean?

h. Does the sample data provide evidence (alpha=.05), that the mean age of Sandy’s customers is indeed over 30?

2. The manager of accounts receivables believes that less than 10% of invoices have at least one error. A random sample of 400 invoices yields 30 invoices with at least one error. Does the sample data provide evidence to support the manager’s claims(using alpha – .10)? In answering this question be sure to address all of the points below.
a. State the null and alternative hypothesis?

b. State the level of significance.

c. Find the critical value or values and clearly show the rejection and non-rejection regions

d. Compute the test statistic

e. Decide whether you can reject Ho and accept Ha or not.

f. Explain and interpret your conclusion in part e.

g. Determine the observed p-valuefor the hypothesis test and interpret this value. What does this mean?

h. Does the sample data provide evidence (alpha = .10) , that less than 10% of invoices have at least one error.

# Hypothesis testing problems

See the attachment for proper formatting of tables and special characters.

Multiple myeloma or blood plasma cancer is characterized by increased blood vessel formulation in the bone marrow that is a prognostic factor in survival. One treatment approach used for multiple myeloma is stem cell transplantation with the patient’s own stem cells. The following data represent the bone marrow microvessel density for a sample of 7 patients who had a complete response to a stem cell transplant as measured by blood and urine tests. Two measurements were taken: the first immediately prior to the stem cell transplant, and the second at the time of the complete response. Use these data to answer questions 1 through 5.

(see attached file)

1. If we wish to determine if the mean bone marrow microvessel density is higher before the stem cell transplant than after the stem cell transplant, the null hypothesis would be
A) H0: ud = 0
B) H0: ud > 0
C) H0: ud < 0
D) H0: ud ≠ 0

2. If we are interested in determining if the mean bone marrow microvessel density is higher before the stem cell transplant than after the stem cell transplant, the alternative hypothesis would be
A) H1: ud = 0
B) H1: ud > 0
C) H1: ud ≤ 0
D) H1: ud ≠ 0

3. Perform an appropriate test of hypothesis to determine if there is evidence, at the .05 level of significance, to support the claim that the mean bone marrow microvessel density is higher before the stem cell transplant than after the stem cell transplant? What is the value of the sample test statistic?
A) z = 1.8424
B) t = 1.8424
C) t = 2.7234
D) p = 2.7234

4. What is the p-value associated with the test of hypothesis you conducted?
A) p = .057403
B) p = .114986
C) p = .942597
D) p = .885014

5. At the .05 level of significance, is there sufficient evidence to conclude that the mean bone marrow microvessel density is higher before the stem cell transplant than after the stem cell transplant?
A) no
B) yes
C) It is impossible to determine

Consider this scenario in answering questions 6 through 8. Results from previous studies showed 79% of all high school seniors from a certain city plan to attend college after graduation. A random sample of 200 high school seniors from this city reveals that 162 plan to attend college. Does this indicate that the percentage has increased from that of previous studies? Test at the 5% level of significance.

6. State the null and alternative hypotheses.
A) H0: u = .79, H1: u > .79
B) H0: p = .79, H1: p ≠ .79
C) H0: p = .79, H1: p > .79
D) H0: p = .79, H1: p > .79

7. Compute the z or t value of the sample test statistic.
A) z = 0.69
B) t = 1.645
C) z = 1.96
D) z = 0.62

A) Do not reject H0
B) Reject H0
C) Cannot determine
D) More seniors are going to college

The marketing manager of a large supermarket chain would like to use shelf space to predict the sales of pet food. For a random sample of 12 similar stores, she gathered the following information regarding the shelf space, in feet, devoted to pet food and the weekly sales in hundreds of dollars. Use these data to answer questions 9 through 11.

(see attached file)

9. What is the equation for the least squares line?
A) Y = 2.63 + 0.724x
B) Y = 1.45 + 0.724x
C) Y = 1.45 + 0.074x
D) Y = 2.63 – 0.174x

10. Compute the coefficient of determination.
A) 0.8270
B) 0.6839
C) 0.3081
D) 0.0009

11. Construct a 95% prediction interval estimate for the weekly sales, in hundreds of dollars, for a store with 8 feet of shelf space devoted to pet food.
A) 2.86 < y < 6.23
B) 1.31 < y < 2.77
C) -0.131 < y < 1.84
D) 1.54 < y < 4.24

A market research study was conducted to compare three different brands of antiperspirant. The results of the study are summarized below. Use a 5% level of significance and test the claim that opinion is independent of brand. Use these data to answer questions 12 and 13.

(see attached file)

12. What is the value of the sample test statistic?
A) x^2 = 19.00
B) x^2 =9.49
C) F = 0.10
D) x^2 = 11.91

A) Opinion and Brand are independent
B) Opinion and Brand are not independent
C) Cannot determine

Customer base data for sporting goods stores
(see attached file)

The data in the above worksheet “CustomerData” includes the monthly sales totals from a random sample of 38 stores in a nation-wide chain of sporting goods stores. All stores in the chain are approximately the same size and carry essentially the same merchandise. Information—as described in the comments in each column—is also provided in this dataset regarding the customer base for each of the 38 stores in the sample. Use these data to answer questions 14 through 18.

14. Assuming a linear relationship exists, formulate a simple linear regression model that estimates the relationship between monthly sales (Y) and median family income (X).
A) Y = 39.17 + 299876.81(X)
B) Y = 299876.81 + 39.17(X)
C) Y = 785476.90 + 43.96(X)
D) Y = 14.07 + 278756.44(X)

15. Compute the coefficient of determination. Enter it, rounded to four decimal places in the blank. ___________

16. At the a = .05 level of significance, is there evidence of a statistically significant linear relationship between monthly sales and median family income?
A) No
B) Yes
C) It cannot be determined

17. Derive a 95% confidence interval estimate for predicting the monthly sales associated with a store located in an area where the median family income is \$35000. Place your limits, rounded to the nearest dollar, in the blanks. Lower limit in the first blank; upper limit in the second blank. Do not use dollar signs, commas, or other punctuation in your responses.
Lower limit = _________________
Upper limit = _________________

18. With respect to the response variable, monthly sales, which predictor variable among those given in the worksheet CustomerData, provides the most explanatory power?
A) Age
B) Growth
C) Income
D) HS
E) College

NFL salaries and bonuses 2000 season
(see the attachment)

Data regarding the salaries and bonuses received by the nearly 1800 players in the National Football League during the 2000 season are provided above. Using these data, perform an appropriate test of hypothesis, at the a = .05 level of significance, to determine whether compensation for players in the NFL is dependent on the team for which they play.

19. What is the value of the sample test statistic?
A) x^2 = 113.15
B) x^2 = 160.47
C) p = 0.0001
D) x^2 = 224.78

A) Salary and team membership are independent
B) Salary and team membership are dependent
C) Cannot determine
D) The Pittsburgh Steelers are the best franchise in the NFL

See attached.

# Hypothesis testing problems

Given that Ho = null hypothesis and Ha= alternative hypothesis then consider the following situations.

1. You are a juror in a murder trial. State the null and alternative hypothesis and explain why. What are two mistakes that can occur here (the two mismatches between what reality is and what the decision is).

2. You are taking a lie detector to prove to your employer that you have not stolen any goods. State the null and alternative hypothesis and explain why. What are two mistakes that can occur here (the two mismatches between what reality is and what the decision is).

3. You are taking a lie detector because your employer wants to prove that you have stolen goods. State the null and alternative hypothesis and explain why. What are two mistakes that can occur here (the two mismatches between what reality is and what the decision is).

4. You are taking a blood test for Gene Z syndrome. State the null and alternative hypothesis and explain why. What are two mistakes that can occur here (the two mismatches between what reality is and what the decision is).

# Hypothesis testing problems

I am currently struggling understanding how to get the right answers for my hypothesis testing chapter 9. Please provide steps on how to obtain the solution? I believe I’m missing several steps:

Doan & Seward edition
9.7 Calculate the test statistic and p-value for each sample.
b. H0: &#960; &#8805; .50 versus H1: &#960; < .50, &#945; = .025, p = .60, n = 90

9.14 The recent default rate on all student loans is 5.2 percent. In a recent random sample of 300 loans
at private universities there were 9 defaults. (a) Does this sample show sufficient evidence that the
private university loan default rate is below the rate for all universities, using a left-tailed test at
&#945; = .01? (b) Calculate the p-value. (c) Verify that the assumption of normality is justified.

9.20 Find the p-value for each test statistic.
c. Two-tailed test, z=&#8722;1.69

9.25 Calculate the test statistic and p-value for each sample. State the conclusion for the specified &#945;.
b. H0: &#956; &#8805; 200 versus H1: &#956; < 200, &#945; = .05, ¯ x = 198, s = 5, n = 25

9.30 In 2004, a small dealership leased 21 Chevrolet Impalas on 2-year leases. When the cars were returned in 2006, the mileage was recorded (see below). Is the dealer’s mean significantly greater than the national average of 30,000 miles for 2-year leased vehicles, using the 10 percent level of significance? Mileage
40,060 24,960 14,310 17,370 44,740 44,550 20,250
33,380 24,270 41,740 58,630 35,830 25,750 28,910
25,090 43,380 23,940 43,510 53,680 31,810 36,780

UOP chpt 9 – Statistics II RES/342

# Hypothesis testing problems

Refer to the baseball data reports………….

# Hypothesis testing problems

1. In a population of typical college students, µ=75 on a statistics final exam (σx=6.4). For 25 students who studied statistics using a new technique, X=72.1. Using two tails of the sampling distribution and the .05 criterion: A.) what is the critical value? B.) Is this sample in the region of rejection? How do you know? C.) Should we conclude that the sample represents the population of typical students? D.) Why?

2. On a standard test of motor coordination, a sports psychologist found that the population of average bowlers had a mean score of 24, with a standard deviation of 6. She tested a random sample of 30 bowlers at Fred’s Bowling Alley and found a sample mean of 26. A second random sample of 30 bowlers at Ethel’s Bowling Alley had a mean of 18. Using the criterion of ρ= .05 and both tails of the sampling distribution, what should she conclude about each sample’s representativeness of the population of average bowlers?

3.) Foofy computes the X(sample mean of Xs, can’t figure out how to make the line above the X) from the data that her professor says is a random sample from population Q. She correctly computes that this mean has a z-score of +41 on the sampling distribution fro population Q. Foofy claims she has proven that this could not be a random sample from population Q. Do you agree of disagree? Why?

# Hypothesis testing problems

Assume that a 2005 poll of 1000 American voters found that 76% of Republicans favored ending the tax on dividend income, as did 42% of Democrats and 54% of Independents. Also assume that Republicans comprise 45% of American voters, Democrats 45% and Independents 10%.

a.What percentage of American voters are in favor of ending the tax on dividend income?

b.Is party affiliation independent of whether one favors ending the tax on dividends?

# Hypothesis testing problems

What test of differences is appropriate in each of the following situations and why ?

(a) Average campaign contributions of Democrats, Republicans, and Independents are to be compared.

(b) Managers and supervisors have responded “yes,” “no,” or “not sure” to an attitude question. Their answers are to be compared.

(c) One-half of a sample receives an incentive in a mail survey. The other half does not. A comparison of response rates is desired.

(d) Stockbrokers in the East, Midwest, and West were asked their annual incomes. Regional comparisons are to be made.

# Hypothesis Testing Problems

Please show all the work for each problem.

Chapter Questions

2. Describe what is measured by the estimated standard error I the bottom of the
independent -measures t statistics?

20. Harris, Schoen, and Hensley (1992) conducted a research study showing how cultural experiences can influence memory. They presented participants with two different versions of stories. One version contained facts or elements that were consistent with a U.S. culture and the second version contained materials consistent with a Mexican culture. The results showed that the participants tended to make errors for the information that was not consistent with their own culture. Specifically, participants from Mexico either forgot or distorted information that was unique to U>S> culture and participants from the United States forgot to or distorted information that unique to Mexican culture. The following data represents results similar to those obtained by Harris, Schoen and Hensley. Is there a significant difference between the two groups? Use a two- tailed test with &#945; = .05

Number of Error Recalling the Mexican Story

n = 20 n = 20
M = 4.1 M= 6.9
SS = 180 SS = 200

22. Steven Schmidt (1994) conducted a series of experiments examining the effects of humor on memory. In one study, participants were given a mix of humorous in addition, non-humorous sentences significantly more humorous sentences were recalled. However, Schmidt argued that the humorous sentences were not necessarily easier to remember, they were simply preferred when participants had a choice between two types of sentences. T tests this argument he switched to an independent -measures designed in which one group got a set of exclusively no humorous sentences. The following data are similar tit he results from the independent -measures study.

Humorous Sentences Nonhumorous Sentences

4 5 2 4 6 3 5 3
6 7 6 6 3 4 2 6
2 5 4 3 4 3 4 4
3 3 5 3 5 2 6 4

A Researcher conducted an independent- measures research study and obtain t= 2.070 with df = 28.

a. How many individuals participants in the entire research study?
b. Using a two -tailed test with &#945; = .05, is there a significant difference between the two treatment condition?
c. Compute r2 to measure the percentage of variance accounted by the treatment effect.

Chapter 11

4.
A researcher conducts an experiment comparing two-treatment condition and obtains data with 10 scores for each treatment condition.
a. If the researcher used an independent-measure designed, how many subjects participated in the experiment?
b. If the researcher used a repeated – measure design how many subjects participated in the experiment.
c. If the researcher used a matched -subjects design, how many subjects participated in the experiment?

10. Research has shown that losing even one night’s sleep can have significant effects on performances of complex tasks such as problem solving (linde & Bergstroem, 1992). To demonstrate this phenomenon a sample of n = 25 college students was given a problem -solving task at noon on one day and again at noon on the following day. The student was not permitted any sleep between the two tests. For each student, the difference between the first and second score was recorded. For this sample the students averaged Md= 4.7 points better on the first test with a variance of s2 = 64 for the difference scores.
a. Do the data indicate a significant change in problem-solving ability? Use a two-tailed test with &#945; =.
b. Compare an estimated Cohen has to measure the size of the effect.

24. A researcher studies the effect of a drug (MAO inhibitor) on the number of nightmares occurring in veterans with post- traumatic stress disorder (PTSD). A sample of PTSD client s records each incidents of a nightmare for I month, and they continue to report each occurrence of a nightmare. For the following Hypothetical dtat, determine whether the MSO inhibitor significance and one-tailed test.

Number of Nightmares

1 month before treatment 1month During treatment

6 1
10 2
3 0
5 5
7 2

# Hypothesis testing problems

Having trouble figuring out how to work some problems from Elementary Statistics. See attachment for problems.

In the following exercises examine the given statement, and then express the null hypothesis H&#959; and alternative hypothesis H1 in symbolic form.

12 The mean top of knee height of a sitting male is 20.7 inches.

15 Plain M&M candies have a mean weight that is at least 0.8535

16 The percentage of workers who got a job through their college is no more than 2%.

In the following exercises, find the critical z values. In each case, assume that the normal distribution applies.

19 Right – tailed test; &#945;= 0.01

20 Left handed test &#945;= 0.05

In the following exercises, test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value or critical value(s), conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value method.

12 Among 734 randomly selected Internet users, it was found that 360 of them use the Internet for making travel plans (based on data from a Gallup poll). Use a 0.01 significance level to test the claim that among Internet users, less than 50% use it for making travel plans. Are the results important for travel agents?

13 Technology is dramatically changing the way we communicate. In 1997, a survey of 880 U.S. households showed that 149 of them use email (based on data from The World Almanac and Book of Facts). Use those sample results to test the claim that more than 15% of U.S. households use email. Use a 0.05 significance level. Is the conclusion valid today?

In the following exercises, test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value or critical value(s), conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value method.

13 Randomly selected statistics students of the author participated in an experiment to test their ability to determine when 1 minute has passed. Forty students yielded a sample mean of 58.3 seconds. Assuming that &#963; = 9.5 seconds, use a 0.05 significance level to test the claim that the population mean is equal to 60 seconds. Based on the result, does there appear to be an overall perception of 1 minute that is reasonably accurate?

17 When 14 different second year medical students at Bellevue Hospital measured the systolic blood pressure of the same person, they obtained the results listed below (in mmHg). Assuming that the population standard deviation is known to be 10 mmHg, use a 0.05 significance level to test the claim that the mean blood pressure is less than 140 mmHg.

138 130 135 140 120 125 120 130 130 144 143 140 130 150

Comparing Variation

11 Researchers conducted a study to determine whether magnets are effective in treating back pain, with results given below. The values represent measurements of pain using the visual analog scale. Use a 0.05 significance level to test the claim that those given a sham treatment (similar to a placebo) have pain reductions that vary more than the pain reductions for those treated with magnets.

Reduction in pain level after sham treatment: n = 20, x = 0.44, s = 3.6
Reduction in pain level after magnet treatment: n = 35, x = 51.3, s = 4.5

# Hypothesis testing problems

A sample of 40 house holds with children from Middleton was randomly selected. The mean length of time was 7.6 years, with a S.D.of 2.3 years. 55 households revealed the mean length of time was 8.1 years with S.D. 2.9 years. At .05 level of sig. can we conclude that students stayed in their district less Brockton students? Use the 5 step Hypothesis.

# Hypothesis testing problems

Customers were waiting in line too long so data was collected. The mean time was 28 minutes. One month later a sample of 127 customers was selected. The mean wait time recorded was 26.9 minutes and the S.D. of the sampling was 8 minutes. Using the .02 level of significance, conduct a 5 step hypothesis testing to determine if the new processes significantly reduced the wait time.

# Hypothesis testing problems

A survey of 1,233 visitors to Mumbai last year revealed that 110 visited a small cafe during their visit. Laura claims that 10% of tourists will include a visit to a cafe. Use a 0.05 significance level to test her claim. Would it be wise for her to use that claim in trying to convince management to increase their advertising spending to travel agents? Explain.

# Hypothesis testing problems –

Dear OTA,

Thanks

1) The MacBurger restaurant chain claims that the waiting time of customers for service is normally distributed, with a mean of 3 minutes and a standard deviation of 1 minute. The quality-assurance department found in a sample of 50 customers at the Warren Road MacBurger that the mean waiting time was 2.75 minutes. At the .05 significance level, can we conclude that the mean waiting time is less than 3 minutes?

2) The management of White Industries is considering a new method of assembling its golf cart. The present method requires 42.3 minutes, on the average, to assemble a cart. The mean assembly time for a random sample of 24 carts, using the new method, was 40.6 minutes, and the standard deviation of the sample was 2.7 minutes. Using the .10 level of significance, can we conclude that the assembly time using the new method is faster?

# Hypothesis testing problems

Show all work solve in excel only.

# Hypothesis Testing Problems

See attached file for proper format.

1. [2%] ONE SAMPLE HYPOTHESIS TEST FOR MEAN: A bowler who has averaged 196 pins in the past year is asked to experiment with a ball made of a new kind of material. If he rolls 25 games with the new ball, averaging 204 pins with a standard deviation of 24.9, can one conclude at a level of significance of .01 that the new ball has improved his game?
1a) Direction = UPPER TAILED / LOWER TAILED / 2-TAILED (circle one)
1b) P-value = ________________
1c) REJECT THE NULL or DO NOT REJECT THE NULL? (circle one)
1d) Can we conclude the ball improved his game? YES or NO (circle one)

2. [2%] ONE SAMPLE HYPOTHESIS TEST FOR PROPORTION: The Webster University librarian believes that more than 60% of the books checked out by students was fictional material. In a random sample of 1000 students who checked books out in the last year, 628 checked out fictional material. What can one conclude about the librarian’s hypothesis at a level of significance of .05?
2a) Direction = UPPER TAILED / LOWER TAILED / 2-TAILED (circle one)
2b) P-value = ________________
2c) REJECT THE NULL or DO NOT REJECT THE NULL? (circle one)
2d) Can we conclude the librarian’s claim is correct? YES or NO (circle one)

3. [2%] TWO SAMPLE HYPOTHESIS TEST FOR MEAN – INDEPENDENT SAMPLES: Eight college students were randomly divided into 2 groups of 4 each to test whether background music reduces studying capacity. Each person was tasked with memorizing a list of 20 words. Group 1 had music playing through earphones they were wearing. Group 2 was not distracted. The following are the number of words correctly remembered by each subject. Test whether the music reduces studying capacity at a .05 level of significance.
Group 1 — DISTRACTED Group 2 – NOT DISTRACTED
Sample mean = 7
Sample size = 4
Sample std.dev. = 2.5 Sample mean = 14
Sample size = 4
Sample std.dev. = 3.5

3a) Direction = UPPER TAILED / LOWER TAILED / 2-TAILED (circle one)
3b) P-value = ________________
3c) REJECT THE NULL or DO NOT REJECT THE NULL? (circle one)
3d) Can we conclude that music reduces studying capacity? YES or NO (circle one)

4. [2%] TWO SAMPLE HYPOTHESIS TEST FOR PROPORTION: Before starting his campaign for mayor, Mr. Emory Board decided to do a study to see if there was a difference in the proportion of registered men and women voters who actually vote (so he would know whom to target his campaign toward). Of the 100 men and 150 women surveyed, 50 men and 100 women admitted to voting. What can he conclude at the .05 level of significance?
4a) Direction = UPPER TAILED / LOWER TAILED / 2-TAILED (circle one)
4b) P-value = ________________
4c) REJECT THE NULL or DO NOT REJECT THE NULL? (circle one)
4d) Can we conclude a difference in voting patterns for men vs. women?
YES or NO (circle one)

5. [2%] TWO SAMPLE HYPOTHESIS TEST FOR PAIRED SAMPLES: In a study of the effectiveness of a reducing diet, the following “before and after” figures (in pounds) were obtained for a sample of 4 adult women in their 30’s. What can we conclude from these figures at a level of significance of .01?
Group 1 — BEFORE Group 2 – AFTER
Woman #1
Woman #2
Woman #3
Woman #4 134
147
178
122 130
140
165
122
5a) Direction = UPPER TAILED / LOWER TAILED / 2-TAILED (circle one)
5b) P-value = ________________
5c) REJECT THE NULL or DO NOT REJECT THE NULL? (circle one)
5d) Can we conclude that the diet worked? YES or NO (circle one)

6. [2%] ANOVA: Three groups of 5 students were tested in their ability to correctly answer a 10-question quiz under different formats. Group 1 had a True/False quiz, Group 2 had a Fill-In quiz, and Group 3 had a Multiple Choice quiz. Their scores were as follows:

True/False Fill-In Multiple Choice
6 3 6
8 5 10
9 6 6
7 7 8
10 5 7

Test whether there was a difference in performance on answering the same general questions under different formats. Use a .05 level of significance.

6a) P-value = ________________
6b) REJECT THE NULL or DO NOT REJECT THE NULL? (circle one)
6c) Can we conclude a difference in means? YES or NO (circle one)
6d) If the null is rejected, which specific differences are statistically significant?
T/F vs. Fill-in Fill-in vs. Multiple Choice T/F vs. Multiple Choice
(circle all that apply)

7. [2%] CHI SQUARE TEST OF INDEPENDENCE: Of a sample of 80 single and married women surveyed, we obtained the following data as to the sizes of cars each one owns (assuming 1 car per person). Test whether car size is independent of marital status at the .01 significance level.
Compact Midsize Luxury TOTAL
Single 8 14 8 30
Married 32 10 8 50
TOTAL 40 24 16 80

7a) P-value = ________________
7b) REJECT THE NULL or DO NOT REJECT THE NULL? (circle one)
7c) Can we conclude that car size is dependent on marital status? YES or NO
(circle one)

8. [3%] CORRELATION & REGRESSION: Dr. A. Nova wanted to test his theory that there was a relationship between one’s attendance and one’s performance on his Sadistics exams. He tracked the number of days absent for each of his students this term along with their course averages (shown below). Test whether there is a correlation between the two at a .05 significance level. Also use the regression model to predict a student’s average if he/she misses 4 classes. BE PREPARED TO ANSWER SIX QUESTIONS REGARDING THE OUTPUT.
Days Absent Course Average
Antonio
Bertram
Cecil
Dudley
Eduardo
Fazzio
Guido
Harvey
Ignatius
Jeremiah 3
1
7
5
0
8
5
3
9
2 85
90
63
78
99
65
80
78
47
88

9. [3%] MULTIPLE LINEAR REGRESSION: Dr. A. Nova conducted a survey to see how well the students performed this semester (measured by their GPA) as a function of their age, gender and course load. The following output shows the first run of multiple linear regression. BE PREPARED TO ANSWER SIX QUESTIONS REGARDING THE OUTPUT. (note: for Gender, 0 = Male, 1 = Female).

10. [3%] FORECASTING: The Surgical Intensive Care Unit would like to be better prepared by forecasting the number of surgical patients they should expect. The past 15 days shows the following numbers of surgeries performed. Conduct a 3-period moving average, an exponential smoothing forecasting using an alpha of .25, and a seasonal forecast with 3 seasons.

Day Surgeries
1 10
2 8
3 12
4 10
5 9
6 14
7 11
8 10
9 15
10 13
11 13
12 16
13 14
14 13
15 18

10a) Forecast for day 16 using 3-period Moving Average = ________________
10b) Forecast for day 16 using Exponential Smoothing (alpha = .25) =________
10c) Forecast for day 16 using Seasonality with 3 seasons = _______________

# Hypothesis Testing Problems

31. A new weight-watching company, Weight Reducers International, advertises that those
who join will lose, on the average, 10 pounds the first two weeks with a standard deviation
of 2.8 pounds. A random sample of 50 people who joined the new weight reduction program
revealed the mean loss to be 9 pounds. At the .05 level of significance, can we
conclude that those joining Weight Reducers on average will lose less than 10 pounds?
Determine the p-value.

32. Dole Pineapple, Inc., is concerned that the 16-ounce can of sliced pineapple is being
overfilled. Assume the standard deviation of the process is .03 ounces. The quality control
department took a random sample of 50 cans and found that the arithmetic mean
weight was 16.05 ounces. At the 5 percent level of significance, can we conclude
that the mean weight is greater than 16 ounces? Determine the p-value.

38. A recent article in The Wall Street Journal reported that the 30-year mortgage rate is now
less than 6 percent. A sample of eight small banks in the Midwest revealed the following
30-year rates (in percent):

4.8 5.3 6.5 4.8 6.1 5.8 6.2 5.6

At the .01 significance level, can we conclude that the 30-year mortgage rate for small
banks is less than 6 percent? Estimate the p-value.

27 A recent study focused on the number of times men and women who live alone buy
take-out dinner in a month. The information is summarized below.

Statistic Men Women
Sample mean 24.51 22.69
Population standard deviation 4.48 3.86
Sample size 35 40

At the .01 significance level, is there a difference in the mean number of times men and
women order take-out dinners in a month? What is the p-value?

46. Grand Strand Family Medical Center is specifically set up to treat minor medical emergencies
for visitors to the Myrtle Beach area. There are two facilities, one in the Little
River Area and the other in Murrells Inlet. The Quality Assurance Department wishes to
compare the mean waiting time for patients at the two locations. Samples of the waiting
times, reported in minutes, follow:

Location Waiting Time
Little River 31.73 28.77 29.53 22.08 29.47 18.60 32.94 25.18 29.82 26.49
Murrell’s Inlet 22.93 23.92 26.92 27.20 26.44 25.62 30.61 29.44 23.09 23.10 26.69 22.31

Assume the population standard deviations are not the same. At the .05 significance level,
is there a difference in the mean waiting time?
52 The president of the American Insurance Institute wants to compare the yearly costs of
auto insurance offered by two leading companies. He selects a sample of 15 families,
some with only a single insured driver, others with several teenage drivers, and pays each
family a stipend to contact the two companies and ask for a price quote. To make the
data comparable, certain features, such as the deductible amount and limits of liability,
are standardized. The sample information is reported below. At the .10 significance level,
can we conclude that there is a difference in the amounts quoted?
BTW – this is a paired t test

Progressive GEICO
Family Car Insurance Mutual Insurance
Becker \$2,090 \$1,610
Berry 1,683 1,247
Cobb 1,402 2,327
Debuck 1,830 1,367
DuBrul 930 1,461
Eckroate 697 1,789
German 1,741 1,621
Glasson 1,129 1,914
King 1,018 1,956
Kucic 1,881 1,772
Meredith 1,571 1,375
Obeid 874 1,527
Price 1,579 1,767
Phillips 1,577 1,636
Tresize 860 1,188

23 A real estate agent in the coastal area of Georgia wants to compare the variation in the
selling price of homes on the oceanfront with those one to three blocks from the ocean.
A sample of 21 oceanfront homes sold within the last year revealed the standard deviation
of the selling prices was \$45,600. A sample of 18 homes, also sold within the last
year, that were one to three blocks from the ocean revealed that the standard deviation
was \$21,330. At the .01 significance level, can we conclude that there is more variation
in the selling prices of the oceanfront homes?

28 The following is a partial ANOVA table.

Complete the table and answer the following questions. Use the .05 significance level.
a. How many treatments are there?
b. What is the total sample size?
c. What is the critical value of F?
d. Write out the null and alternate hypotheses.
e. What is your conclusion regarding the null hypothesis?

19. In a particular market there are three commercial television stations, each with its own
evening news program from 6:00 to 6:30 P.M. According to a report in this morning’s local
newspaper, a random sample of 150 viewers last night revealed 53 watched the news
on WNAE (channel 5), 64 watched on WRRN (channel 11), and 33 on WSPD (channel 13).
At the .05 significance level, is there a difference in the proportion of viewers watching
the three channels?

20. There are four entrances to the Government Center Building in downtown Philadelphia.
The building maintenance supervisor would like to know if the entrances are equally utilized.
To investigate, 400 people were observed entering the building. The number using
each entrance is reported below. At the .01 significance level, is there a difference in the
use of the four entrances?

Entrance Frequency
Main Street 140
Cherry Street 90
Walnut Street 50
Total 400

How do you classify statistical findings in order of power: nominal, ordinal, interval, and ratio?
Give example by making up values.

# Hypothesis testing problems

1. In a one-way ANOVA, there are three treatments with n1 = 6, n2 = 6 and n3 = 5. The rejection region for this test at the 5% level of significance is
A. F > 4.86
B. F > 3.74
C. F > 4.97
D. F > 3.81

2. The following data show samples of three chain stores in three different locations in one town and the amount of dollars spent per customer per visit.

Store A Store B Store C
30 42 30
14 28 14
22 20 20
18 35 16
26 49 15
25 28

An analysis of variance was performed on these data, resulting in the ANOVA table below. Consider these data and answer the questions that follow.

Source df SS MS

Method 682.79

Error 989.00

Total Critical value = 3.74

a. Fill in the degrees of freedom for Method, Error and Total.
b. Calculate and fill in the Mean Square figures for Method and Error.
c. Calculate the F* statistic for this ANOVA.
d. Summarize your conclusions and results of the test.

3. In a one-way ANOVA, if the test is conducted and the null hypothesis is rejected, what does this indicate?

A. The normal distribution should have been used instead of the F-distribution to determine the critical values of the test
B. All population means are different from one another.
C. At least one of the population means are different
D. All the population means are equal.

4. Choose a variable and collect data for at least three different groups (samples). Compare the means of the three groups using the one-way ANOVA technique. Display all data and show all work. Complete the following:

a. Write a brief statement of the purpose of the study
b. Define the population that is being studied.
c. State how the sample was selected from the population.
d. What &#61537; value did you use?
e. State the hypotheses.
f. What was F test value?
g. State the decision that was made based upon the test value.
h. Summarize the results of the study and decision.

You may obtain raw data from the random number table in the appendix section of your text or from any other sources, including sources on the World Wide Web.

# Hypothesis testing problems

1. Classify the following as independent or dependent samples:

a. The effectiveness of two blood pressure medicines on two groups of patients.
b. Measures of gas mileage and speed for a group of race cars.
c. Scores of a group of nurses on the NCLEX nursing license exam.

a. Explain the difference between testing a single mean and testing the difference between two means.

b. What two assumptions must be met when one is using z test to test differences between two means?

c. When can the sample standard deviations s1 and s2 be used in place of the population standard deviations &#61555;1 and &#61555;2?

3. Choose a variable. Before you simulate collecting the data, decide what a likely average might be and list all data in part e.; then complete the following:

a. Write a brief statement of purpose of the study and the population to be studied
b. State the hypotheses for the study
c. Select an &#61537; value
d. Display all the raw data
e. Decide which statistical test is appropriate and compute the test statistic (z or t). Find the critical values(s)

f. State the decision and summarize the results in a paragraph.

You may obtain raw data from the random number table in the appendix section of your text or from any other sources; including sources on the World Wide Web.

a. In what ways is the t distribution similar to the standard normal distribution?

b. In what ways is the t distribution different from the standard normal distribution?
Please specify how the formula for the t test differs from the formula for the z test?

5. Complete the following:

a. Select a variable. Compare the mean of the variable for a sample of 30 for one group with the mean of the variable for a sample of 30 for a second group. Show a hypothetical set of data with a hypothetical mean and standard deviation and show all calculations for conducting a z test with these data.

b. Select a variable. Compare the mean of the variable for a sample of 10 for one group with the mean of the variable for a sample of 10 for a second group. Show a hypothetical set of data with a hypothetical mean and standard deviation and show all calculations for conducting a t test with these data.

c. Select a variable that will enable you to compare proportions of two groups. Use sample sizes of at least 30. Use the z test for proportions to analyze the data.

You may obtain raw data from the random number table in the appendix section of your text or from any other sources; including sources on the World Wide Web.

# Hypothesis testing problems

The Employment and Training Administration reported the U.S. mean unemployment insurance benefit of \$238 per week (The World Almanac 2003). A researcher in the state of Virginia anticipated that sample data would show evidence that the mean weekly unemployment insurance benefit in Virginia was below the national level. For a sample of 136 individuals, the sample mean weekly unemployment insurance benefit was \$229 with a sample standard deviation of \$70.

a) In proper notation, state the hypotheses of this test.

b) What is the rejection rule at the default value of &#945;?

c) Show your calculation of the test statistic. ______ = ______________

d) What is the conclusion about the issue in question ?

# Hypothesis testing problems

See the attached file.
1) Clark Heter is an industrial engineer at Lyons Products…..

2) Two boats, the Prada (Italy), and the Oracle (U.S.A.) are competing for a spot in the upcoming America’s Cup Race…

# Hypothesis testing problems

1) Find the expected values of the following probabilities……
2) In a population of test scores not known to be probability distributions….

5) Using the sample limit theorem……

8) The null hypothesis that — equals 75 for a sample of 25 subjects….
9) Test the null hypothesis that —- equals 50 for a sample where N = 36
10) After six months in office, a U.S. Senator…..

# Hypothesis testing problems

Question 1
The SAT scores of entering freshmen at X University have a normal distribution with mean &#956;1 = 1200 and standard deviation &#963;1 = 90, while the SAT scores of entering freshmen at Y University have a normal distribution with mean &#956;2 = 1215 and standard deviation &#963;2 = 110. Independent random samples of 100 freshmen are selected from each university. The probability that the sample mean from X University exceeds the sample mean from Y University is

1)0.1446.
2)0.0475.
3)0.2913
4)0.8554.

Question 2
A sociologist is studying the effect on the divorce rate of having children within the first three years of marriage. She selects a random sample of 400 couples who were married for the first time between 1990 and 1995 with both members of the couple aged 20 to 25. Of the 400 couples, 220 had at least one child within the first three years of marriage. Of the couples who had children, 83 were divorced within five years, while of the couples who didn’t have children, 52 were divorced within five years. Let p1 and p2 be the proportions of couples married in this time frame and divorced within five years who had children and didn’t have children, respectively. The sociologist hypothesized that having children early would increase the likelihood of a couple being divorced. She tested H0: p1 = p2 against the one-sided alternative Ha: p1 > p2 and obtained a P-value of 0.0314. Which of the following statements is a correct interpretation of this result?

1) If you want to reduce your chances of getting divorced, it is best not to marry until you are closer to 30 years of age.

2) If you want to reduce your chances of getting divorced, it is best to wait several years before having children.

3) You have a better chance of staying married if yo do not have children.

4) There is evidence of an association between having children early in a marriage and divorce rate.

Question 3
For a simple random sample of 100 cars of a certain popular model in 2003, it was found that 20 had a certain minor defect in the brakes. For an independent SRS of 400 cars of the same model in 2004, it was found that 50 had the same defect. Let p1 and p2 be the proportions of all cars of this model in 2003 and 2004, respectively, that have the defect. We wish to test H0: p1 = p2 against Ha: p1 > p2. For this test, the (approximate) P-value is

1)0.1345
2)0.0418.
3)0.0536.
4)0.0268.

Question 4
When testing a hypothesis, you are actually,

1) finding out whether there is a real difference between two sample statistics.

2) evaluating the sizes of the population statistics (e.g. the mean or proportion).

3) finding an estimate of the probability that the difference between two statistics is 0.

4) None of the above.

Question 5
In hypothesis testing the null hypothesis

1)the problems in the book will always state a null hypothesis.

2)the alternative hypothesis is the hypothesis that says nothing is happening.

3)you choose a null hypothesis based on whether or not you want to find good results.

4)you should use a two-tailed test if you are unsure about whether a one or two-tailed test is appropriate.

Question 6
You are taking a quiz with 10 multiple choice questions and each questions has 4 possible answers. If you assume that the questions are independent, what is the standard deviation for quiz scores?

1)less than 1.

2)1.875

3)1.37

4)2.68

# Hypothesis testing problems

1.A researcher collects infant mortality data from a random sample of villages in a certain country. It is claimed that the average death rate in this country is the same as that of a neighboring country, which is known to be 17 deaths per 1000 live births. To test this claim using a test of hypotheses, what should the null and alternative hypotheses be?

2.The distribution of times that a company’s technicians take to respond to trouble calls is normal with mean &#956; and standard deviation &#963; = 0.25 hours. The company advertises that its technicians take an average of no more than 2 hours to respond to trouble calls from customers. We wish to conduct a test to assess the amount of evidence against the company’s claim. In a random sample of 25 trouble calls, the average amount of time that technicians took to respond was 2.1 hours. From these data, the P-value of the appropriate test is?

3.A local teachers’ union claims that the average number of school days missed due to illness by the city’s school teachers is fewer than 5 per year. A random sample of 28 city school teachers missed an average of 4.5 days last year, with a sample standard deviation of 0.9 days. Assume that days missed follow a normal distribution with mean &#956;. A test conducted to see whether there is evidence to support the union’s claim will have a P-value of?

4.Jamaal, a player on a college basketball team, made only 50% of his free throws last season. During the off-season, he worked on developing a softer shot in the hope of improving his free-throw accuracy. This season, Jamaal made 54 of 95 free throws. Can we conclude that Jamaal’s free-throw percentage p this season is significantly different from last year’s percentage? The approximate P-value for an appropriate test is?

5.Which of the following would have no effect on the P-value of a z test for a population proportion p?
a) increasing the sample size
b) decreasing the significance level of the test, &#945;
c) getting a different value of the sample proportion from the sample data
d) changing the null hypothesis

6. As part of a promotion for a new type of cracker, free samples are offered to shoppers in a local supermarket. The probability that a shopper will buy a package of crackers after tasting the free sample is 0.2. Different shoppers can be regarded as independent trials. Let be the sample proportion of the next n shoppers that buy a packet of crackers after tasting a free sample. How large should n be so that the standard deviation of is no more than 0.01?
a)4
b)16
c)64
d)1600

# Hypothesis testing problems

Comparing ages of a Marathon Runners:
Use a 0.05 significance level to test the claim that for the runners in the New York City marathon, men and women have ages with different amounts of variation.

# Hypothesis testing problems

A U.S. Navy recruiting center knows from past experience that the heights of its recruits are normally distributed with mean 68 inches. The recruiting center wants to test the claim that the average height of this year’s recruits is greater than 68 inches. To do this, recruiting personnel take a random sample of 64 recruits from this year and record their heights (in inches). The data is provided in the file P10_04.xlsx.

# Hypothesis Testing Problems

1. For the samples summarized below, test the hypothesis at =.05 that the two variances are equal.
Variance Number of data values
Sample 1 25 9
Sample 2 9 19

2. A random group of apartments was selected from a city to analyze the number of bedrooms they have. Is there evidence to reject the hypothesis that the apartments are equally distributed between 1-bedroom, 2-bedroom, and 3-bedroom apartments, at alpha = .05?
Year in school 1 bedroom 2 bedrooms 3 bedrooms
Number of students 11 9 14

3. A marketing firm asked a random set of married and single men as to how much they were willing to spend for a vacation. At alpha = .05, is a difference in the two amounts?
Married men Single men
Sample size 50 50
Mean spending 380 325
Sample variance 6000 9000

4. An anatomy teacher hypothesizes that the final grades in her class are distributed as 10% A’s, 23% B’s, 45% C’s, 14% D’s, and 8% F’s. What is the critical value if at the end of the semester she has the following grades? Use a=0.05.
A B C D F
6 14 22 8 4

# Hypothesis testing problems

1) What are the five steps involved in classic hypothesis testing?

2) In general, what is a “Critical Value” or “Cut-Off Score” of a test statistic?
What are the critical values of z for a two-tailed test (.05)?
What are the critical values of z for a one-tailed test (.05)?
What are the critical values of z for a two-tailed test (.01)?

3. a) I measure writing ability in 4th year students at Cosmopolitan and compare those measures with those of 1st year students. What is my Null Hypothesis?

b) I measure Life Satisfaction in a group of cancer survivors and compare their Life Satisfaction scores with those from a people who did not contract cancer.
What is my Null Hypothesis?

4. When we reject the null hypothesis, what are we rejecting? (Hint: Do NOT say that you are rejecting the Null Hypothesis.)

5. What are alpha ( &#945; ) and beta ( &#946; )?

6. I am conducting an experiment that examines learning as a function of study time. One group studies 5 minutes and the other group studies 7 minutes. When I look at my data, I CANNOT reject the Null Hypothesis. What can I do to get more power

# Hypothesis Testing Problems

Note: Methods of computation could include the usage of Excel®, SPSS®, Lotus®, SAS®, MINITAB®, or by hand computation.

Chapter 12: Exercises 10 & 11

10) The manager of a computer software company wishes to study the number of hours senior executives spend at their desktop computers by type of industry. The manager selected a sample of five executives from each of three industries. At the .05 significance level, can she conclude there is a difference in the mean number of hours spent per week by industry?

Banking Retail Insurance
12 8 10
10 8 8
10 6 6
12 8 8
10 10 10

11) Given the following sample information, test the hypothesis that the treatment means are equal at the .05 significance level.

Treatment 1 Treatment 2 Treatment 3

8 3 3
11 2 4
10 1 5
3 4
2

a. State the null hypothesis and the alternate hypothesis.
b. What is the decision rule?
c. Compute SST, SSE, and SS total.
d. Complete an ANOVA table.
e. State your decision regarding the null hypothesis.
f. If H0 is rejected, can we conclude that treatment 1 and treatment 2 differ? Use the 95 percent level of confidence.

Chapter 15: Exercises 10 & 19

10) The chief of security for the Mall of the Dakotas was directed to study the problem of missing goods. He selected a sample of 100 boxes that had been tampered with and ascertained that for 60 of the boxes, the missing pants, shoes, and so on were attributed to shoplifting. For 30 other boxes employees had stolen the goods, and for the remaining 10 boxes he blamed poor inventory control. In his report to the mall management, can he say that shoplifting is twice as likely to be the cause of the loss as compared with either employee theft or poor inventory control and that employee theft and poor inventory control are equally likely? Use the .02 significance level.

19) In a particular market there are three commercial television stations, each with its own evening news program from 6:00 to 6:30 P.M. According to a report in this morning’s local newspaper, a random sample of 150 viewers last night revealed 53 watched the news on WNAE (channel 5), 64 watched on WRRN (channel 11), and 33 on WSPD (channel 13). At the .05 significance level, is there a difference in the proportion of viewers watching the three channels?

# Hypothesis testing problems

The Web-based company Henrietta Balloons has a goal of processing 96% of its orders on the same day they are received.

If 95 out of the next 100 orders were processed on the same day, would this prove that they are exceeding their goal, using a 90% confidence level?

A. Choose the Hypothesis

B. Specify the Decision Rule

C. Calculate the Test Statistic

D. Make the Decision

E. Give an interpretation of the Decision

F. P-value Method
1. Calculate the P-value, what is it?

2. Does that P-value support the Decision in Part D?

# Hypothesis Testing Problems

For each problem below, answer the following

1. State the Ho
2. State the H1
3. Find the critical value
4. Determine the test statistic. Explain
5. State the decision rule
6. Show the decision rule graphically
7. Determine the computed value of the test statistic
8. Determine the p-value
10. Interpret the decision

1. Tom Sevits is the owner of the Appliance Patch. Recently Tom observed a difference in the
dollar value of sales between the men and women he employs as sales associates. A sample
of 40 days revealed the men sold a mean of \$1,400 worth of appliances per day with a
standard deviation of \$200. For a sample of 50 days, the women sold a mean of \$1,500
worth of appliances per day with a standard deviation of \$250. At the .05 significance level
can Mr. Sevits conclude that the mean amount sold per day is larger for the women?

2. Of 150 adults who tried a new peach-flavored peppermint patty, 87 rated it excellent. Of 200
children sampled, 123 rated it excellent. Using the .10 level of significance, can we conclude
that there is a significant difference in the proportion of adults and the proportion of children
who rate the new flavor excellent?

3. The production manager at Bellevue Steel, a manufacturer of wheelchairs, wants to compare
the number of defective wheelchairs produced on the day shift with the number on the
afternoon shift. A sample of the production from 6 day shifts and 8 afternoon shifts revealed
the following number of defects.
Day 5 8 7 6 9 7
Afternoon 8 10 7 11 9 12 14 9
At the .05 significance level, is there a difference in the mean number of defects per shift?

4. Advertisements by Sylph Fitness Center claim that completing their course will result in
losing weight. A random sample of eight recent participants showed the following weights
before and after completing the course. At the .01 significance level, can we conclude the
students lost weight?

Name Before After
Hunter 155 154
Cashman 228 207
Mervine 141 147
Massa 162 157
Creola 211 196
Peterson 164 150
Redding 184 170
Poust 172 165

5. The Grand Strand Family Medical Center is specifically set up to treat minor medical emergencies
for visitors to the Myrtle Beach area. There are two facilities, one in the Little River
Area and the other in Murrells Inlet. The Quality Assurance Department wishes to compare
the mean waiting time for patients at the two locations. Samples of the waiting times, reported
in minutes, follow:
Location Waiting Time
Little River 31.73 28.77 29.53 22.08 29.47 18.60 32.94 25.18 29.82 26.49
Murrells Inlet 22.93 23.92 26.92 27.20 26.44 25.62 30.61 29.44 23.09 23.10 26.69 22.31

At the .05 significance level, is there a difference in the mean waiting time?

# Hypothesis testing problems

Please see attached for fully formatted questions.
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12. The American Sugar Producers Association wants to estimate the mean yearly sugar consumption. A sample of 16 people reveals the mean yearly consumption to be 60 pounds with a standard deviation of 20 pounds.
a. What is the value of the population mean? What is the best estimate of this value?
b. Explain why we need to use the t distribution. What assumption do you need to make?
c. For a 90 percent confidence interval, what is the value of t?
d. Develop the 90 percent confidence interval for the population mean.
e. Would it be reasonable to conclude that the population mean is 63 pounds?

28. A processor of carrots cuts the green top off each carrot, washes the carrots, and inserts six to a package. Twenty packages are inserted in a box for shipment. To test the weight of the boxes, a few were checked. The mean weight was 20.4 pounds, the standard deviation 0.5 pounds. How many boxes must the processor sample to be 95 percent confident that the sample mean does not differ from the population mean by more than 0.2 pounds?

Lind Chapter 10:

6. The MacBurger restaurant chain claims that the waiting time of customers for service is normally distributed, with a mean of 3 minutes and a standard deviation of 1 minute. The quality-assurance department found in a sample of 50 customers at the Warren Road
MacBurger that the mean waiting time was 2.75 minutes. At the .05 significance level, can we conclude that the mean waiting time is less than 3 minutes?

18. The management of White Industries is considering a new method of assembling its golf cart. The present method requires 42.3 minutes, on the average, to assemble a cart. The mean assembly time for a random sample of 24 carts, using the new method, was 40.6 minutes, and the standard deviation of the sample was 2.7 minutes. Using the .10 level of significance, can we conclude that the assembly time using the new method is faster?

Lind Chapter 11:
24. Clark Heter is an industrial engineer at Lyons Products. He would like to determine whether there are more units produced on the afternoon shift than on the day shift. A sample of 54 day-shift workers showed that the mean number of units produced was 345, with a standard deviation of 21. A sample of 60 afternoon-shift workers showed that the mean number of units produced was 351, with a standard deviation of 28 units. At the .05 significance level, is the number of units produced on the afternoon shift larger?

38. Two boats, the Prada (Italy) and the Oracle (U.S.A.), are competing for a spot in the upcoming America’s Cup race. They race over a part of the course several times. Below are the sample times in minutes. At the .05 significance level, can we conclude that there is a difference in their mean times?
Boat Times (minutes)
Prada (Italy) 12.9 12.5 11.0 13.3 11.2 11.4 11.6 12.3 14.2 11.3
Oracle (U.S.A.) 14.1 14.1 14.2 17.4 15.8 16.7 16.1 13.3 13.4 13.6 10.8 19.0

Lind Chapter 12:
30. There are four auto body shops in a community and all claim to promptly serve customers. To check if there is any difference in service, customers are randomly selected from each repair shop and their waiting times in days are recorded. The output from a statistical software package is:
Summary
Groups Count Sum Average Variance
Body Shop A 3 15.4 5.133333 0.323333
Body Shop B 4 32 8 1.433333
Body Shop C 5 25.2 5.04 0.748
Body Shop D 4 25.9 6.475 0.595833

ANOVA
Source of Variation SS df MS F p-value
Between Groups 23.37321 3 7.791069 9.612506 0.001632
Within Groups 9.726167 12 0.810514
Total 33.09938 15

Is there evidence to suggest a difference in the mean waiting times at the four body shops? Use the .05 significance level.

Lind Chapter 15:

12. For many years TV executives used the guideline that 30 percent of the audience were watching each of the prime-time networks and 10 percent were watching cable stations on a weekday night. A random sample of 500 viewers in the Tampa-St. Petersburg, Florida, area last Monday night showed that 165 homes were tuned in to the ABC affiliate, 140 to the CBS affiliate, 125 to the NBC affiliate, and the remainder were viewing a cable station. At the .05 significance level, can we conclude that the guideline is still reasonable?

26. A study regarding the relationship between age and the amount of pressure sales personnel feel in relation to their jobs revealed the following sample information. At the .01 significance level, is there a relationship between job pressure and age?

Degree of Job Pressure
Age (years) Low Medium High
Less than 25 20 18 22
25 up to 40 50 46 44
40 up to 60 58 63 59
60 and older 34 43 43

# Hypothesis Testing Problems

Chapter 10
1. Rutter Nursery Company packages its pine bark mulch in 50-pounds bags. From a long history, the production department reports that the distribution of the bag weights follows the normal distribution and the standard deviation of this process is 3 pounds per bag. At the end of each day, Jeff Rutter, the production manager, weighs 10 bags and computes the mean weight of the sample. Below are the weights of 10 bags from todays’ production.

45.6 47.7 47.6 46.3 46.2 47.4 49.2 55.8 47.5 48.5

a. Can Mr. Rutter conclude that the mean weight of the bags is less than 50 pounds? Use the 0.01 significance level. (show all work)
b. In a brief report, tell why Mr. Rutter can use the Z distribution as the test statistic.
c. Compute the p-value (SHOW ALL WORK)

2. According to a recent survey, Americans get a mean of 7 hour of sleep per night. A random sample of 50 students at West Virginia University revealed the mean number of hours slept last night was 6 hours and 48 minutes (6.8 hours). The standard deviation of the sample was 0.9 hours. Is it reasonable conclude that students at West Virginia sleep less than the typical American? Compute the p-value. (show all work).

3. In recent years the interest rate on home mortgages has declined to less than 6.0 percent. However, according to a study by the federal Reserve Board the rate charges on credit card debt is more than 14 percent. Listed below is the interest rate charged on a sample of 10 credit cards.

14.6 16.7 17.4 17.8 15.4 13.1 15.8 14.3 14.5

Is it reasonable to conclude the mean rate charges is greater than 14 percent? Use the 0.01 significance level. (show all work)

Chapter 12
22. A large company is organized into three functional areas: manufacturing, marketing, and research and development. The employees claim that the company pays women less than men for similar jobs. The company randomly selected four males and four females in each area and recorded their weekly salaries in dollars

Area/Gender Female Male
Manufacturing 1016, 1007, 875, 968 978, 1056, 982, 748
Marketing 1045, 895, 848, 904 1154, 1091, 878, 876
Research and Development 770, 733, 844, 771 926, 1055, 1066, 1088

A. Draw the interaction graph. Based on your observations, is there an interaction effect. Based on the graph, describe the interaction effect of gender and area on salary.
B. Use the 0.05 level for gender, area, and interaction effects on salry. Report the statistical results
C. Compare the male and female mean sales for each area using statistical techniques. What do you recommend to the distributor?

29. A Consumer organization wants to know whether there is a difference in the price of a particular toy at three different types of stores. The price of the toy was checked in a sample of five discount stores, five variety stores, and five department stores. The results are shown below. Use the 0.05 significance level. (SHOW ALL WORK)

Discount Variety Department
\$12 \$15 \$19
13 17 17
14 14 16
12 18 20
15 17 19

Chapter 11

1. The federal government recently granted funds for a special program designed to reduce crime n high-crime areas. A study of the results of the program in eight high-crime areas of Miami, Florida, yielded the following results.

Numbers of Crimes by Area
A B C D E F G H
Before 14 7 4 5 17 12 8 9
After 2 7 3 6 8 13 3 5

Has there been a decrease in the number of crimes since the inauguration of the program? Use the 0.01 significance level. Estimate the p-value. (show all work)

2. The Engineering Department at Sims Software, Inc., recently developed two chemical solutions designed to increase the usable life of computer disks. A sample of disks treated with the first solution lasted 86,78,66,83,84,81,109,65, and 102 hours. Those treated with the second solution lasted 91, 71, 75, 76, 87, 79, 73, 76, 79, same. At the 0.10 significance level, can we conclude that there is a difference in the length of time the two types of treatment lasted?

3. Lester Hollar is vice president for human resources of a large manufacturing company. In recent years he has noticed an increase in absenteeism that he thinks is related to the general health of the employees. Four years ago, in an attempt to improve the situation, he began a fitness program in which employees exercise during their lunch hour. To evaluate the program, he selected a random sample of eight participants and found the number of days each absent in the six months before the exercise program began and in the last six months. Below are the results. At the 0.05 significance level, can he conclude that the number of absences has declined? Estimate the p-value.

Employee Before After
1 6 5
2 6 2
3 7 1
4 7 3
5 4 3
6 3 6
7 5 3
8 6 7

# Hypothesis Testing Problems

MLB 1
A study was conducted to determine if persons in surburan district I have a different mean income from those in district II. A random sample of 50 homeowners was taken in district I. Although 50 homeowners were to be interviewed in district II also, one person refused to provide the information requested. So only 49 observations were obtained from District II. The data produced sample means and variances as shown below. Use these data to test if mean incomes for the two districts are different. Use alpha = .05. Give results f test and p-value.

District I District II
Sample Size 50 49 97
Sample Mean (in thousands \$) 14.27 12.78
Sample Variances 8.74 6.58

MLB 2
The variability in the potency of five grain aspirin tablets differs from one brand to another. An interest research group would like to compare brand C, a new product recently released, to brand B the current best seller. Random samples of 41 tablets are obtained from bottles of each of the brands. The potency results are given in the table below. Use these data to test the hypothesis that the population variances of brands B and C are not equal and that the alternative hypothesis is that brand B has more variability in potency than brand C. Use alpha = .01

1. Value of calculated statistic.
2. Value of critical statistic
3. Result of hypothesis test
Brand B Brand C

Sample Size 41 41
Sample Mean 60.2 60.5
Sample Variance 2.2 0.98

MLB3
A total of 210 emphysema patients entering a clinic over a one year period were treated with one of two drugs (A,B) for a period of one week. After this period of time each patient’s condition was rated as either greatly improved, improved, or no changed. See table below for results. Are the patients rating dependent upon the drug product used? Create contingency table and give results of test. Alpha = .05.

Patient Condition
Drug No Change Improved Greatly Improved
A 20 35 45
B 15 45 50

# Hypothesis Testing Problems

See attached problem set 3 and Also some of these reference data sets that came on a disk with our book.

8 questBusiness Applications Problem Set Three

Excel files needed for these problems can be found on the CD that came with your text.

1. Data File ERWAITING contains the waiting times in minutes for 15 randomly selected patients at a hospital main emergency room facility and at three satellite facilities.

a. At the .05 level of significance, is there evidence that the mean waiting time at the main facility is more than one hour?

Complete the following:
1. State H0.
2. State H1.
3. State the value of &#945;.
4. State the value of the test statistic.
5. State the p-value.
6. State the decision in terms of H0 and why.
7. State the decision in terms of the problem.

b. Suppose you use a .01 level of significance instead of a .05 level. Without doing the problem again, would the result be different from that in part (a)? Explain your answer.

2. A Wall Street Journal article suggests that age bias is becoming an even bigger problem in the corporate world. In 2001, an estimated 78% of executives believed that age bias was a serious problem. In a 2004 study by ExecuNet, 82% of the executives surveyed considered age bias a serious problem. The sample size for the 2004 study was not disclosed. Suppose 50 executives were surveyed.

a. At the .05 level of significance, is there evidence that the proportion of executives who believed age bias was a serious problem increased between 2001 and 2004, that is, is there evidence that the proportion of executives who believed age bias to be a serious problem in 2004 is greater than 78%?

Complete the following:
1. State H0.
2. State H1.
3. State the value of &#945;.
4. State the value of the test statistic.
5. State the p-value.
6. State the decision in terms of H0 and why.
7. State the decision in terms of the problem.

b. Explain the meaning of the p-value in this problem.

c. Suppose the sample size used was 1000. Does that change the conclusion you reached in part (a)? How?

d. Discuss the effect that sample size had on the outcome of this analysis and, in general, on the effect sample size plays in hypothesis-testing.

3. The data file RESTAURANTS contains the ratings for food, décor, service, and price per person for a sample of 50 restaurants located in an urban area and 50 restaurants located in a suburban area. At the .05 level of significance, is there evidence of a difference in the mean food rating between urban and suburban restaurants?

Complete the following:
1. State H0.
2. State H1.
3. State the value of &#945;.
4. State the value of the test statistic.
5. State the p-value.
6. State the decision in terms of H0 and why.
7. State the decision in terms of the problem.

4. A newspaper article discussed the opening of a Whole Foods Market in the Time-Warner building in New York City. The data in file WHOLEFOODS1 compares the prices of some kitchen staples at the Whole Foods Market and at the Fairway Market located about 15 blocks from the Time-Warner building.

a. At the .01 level of significance, is there evidence that the mean price is higher at Whole Foods Market than at the Fairway supermarket?

Complete the following:
1. State H0.
2. State H1.
3. State the value of &#945;.
4. State the value of the test statistic.
5. State the p-value.
6. State the decision in terms of H0 and why.
7. State the decision in terms of the problem.

b. What assumption is necessary about the population distribution in order to perform the test in (a)?

c. Construct a 99% confidence interval estimate of the difference in price between Whole Foods and Fairway. Do the results of the confidence interval and the hypothesis test agree? Explain.

5. As more Americans use cell phones, they question where it is okay to talk on cell phones. The following is a table of results, in percentages, for 2000 and 2006. Suppose the survey was based on 100 respondents in 2000 and 100 respondents in 2006.

Year
OKAY TO TALK ON A CELL PHONE IN A 2000 2006
Bathroom 39 38
Movie/theater 11 2
Car 76 63
Supermarket 60 66
Public transit 52 45
Restaurant 31 21

a. At the .05 level of significance, if there evidence that the proportion of Americans who thought it was okay to use a cell phone in a car in 2000 is significantly greater than the proportion of Americans who thought it was okay to use a cell phone in a car in 2006?

Complete the following:
1. State H0.
2. State H1.
3. State the value of &#945;.
4. State the value of the test statistic.
5. State the p-value.
6. State the decision in terms of H0 and why.
7. State the decision in terms of the problem.

b. Construct a 95% confidence interval estimate of the difference between the proportion of Americans who thought it was okay to use a cell phone in a car in 2000 and the proportion of Americans who thought it was okay to use a cell phone in a car in 2006. Do the results of the hypothesis test and confidence interval agree? Explain.

6. Nine experts rated four brands of Colombian coffee in a taste-testing experiment. A rating on a 7-point scale (1 = extremely unpleasing, 7 = extremely pleasing) is given for each of the four characteristics: taste, aroma, richness, and acidity. The data in file COFFEE give the ratings for four brands of coffee.

a. At the .05 level of significance, is there evidence of a difference in the mean ratings for the four brands of coffee?

Complete the following:
1. State H0.
2. State H1.
3. State the value of &#945;.
4. State the value of the test statistic.
5. State the p-value.
6. State the decision in terms of H0 and why.
7. State the decision in terms of the problem.

b. If appropriate, determine which brands differ.

c. One assumption of ANOVA is that the variances of the populations are equal. At the .05 level of significance, is there evidence of a difference in the variation in the ratings of the four brands of coffee?

Complete the following:
1. State H0.
2. State H1.
3. State the value of &#945;.
4. State the value of the test statistic.
5. State the p-value.
6. State the decision in terms of H0 and why.
7. State the decision in terms of the problem.

7. The health-care industry and consumer advocates are at odds over the sharing of a patient’s medical records without the patient’s consent. The health-care industry believes that no consent should be necessary to openly share data among doctors, hospitals, pharmacies, and insurance companies. Suppose a study is conducted in which 600 patients are randomly assigned, 200 each, to three “organizational groupings”-insurance companies, pharmacies, and medical researchers. Each patient is given material to read about the advantages and disadvantages concerning the sharing of medical records within the assigned “organizational grouping.” Each patient is then asked, “would you object to the sharing of your medical records with…” and the results are recorded in the cross-classification table below.

Organizational Grouping
OBJECT TO SHARING INFORMATION Insurance Pharmacy Research
Yes 40 80 90
No 160 120 110

a. Is there evidence of a difference in the proportions who object to sharing information among the organizational groupings? (Use &#945; = .05.)

Complete the following:
1. State H0.
2. State H1.
3. State the value of &#945;.
4. State the value of the test statistic.
5. State the p-value.
6. State the decision in terms of H0 and why.
7. State the decision in terms of the problem.

b. If appropriate, us the Marascuilo procedure and &#945; = .05 to determine which groups are different.

8. USA Today reported on preferred types of office communication by different age groups. Suppose the results were based on a survey of 500 respondents in each age group. The results are cross-classified in the following table:

Type of Communication Preferred
AGE GROUP GroupMeetings Face-to-FaceMeetings with Individuals E-mails Other Total
Generation X 180 260 50 10 500
Generation Y 210 190 65 35 500
Boomer 205 195 65 35 500
Mature 200 195 50 55 500
Total 795 840 230 135 2000

At the .05 level of significance, is there evidence of a relationship between age group and type of communication preferred?

Complete the following:
1. State H0.
2. State H1.
3. State the value of &#945;.
4. State the value of the test statistic.
5. State the p-value.
6. State the decision in terms of H0 and why.
7. State the decision in terms of the problem.

# Hypothesis testing problems

The results of a recent study regarding smoking and three types of illness are shown below. The illnesses are Emphysema, Heart Problem, and Cancer. Under nonsmokers there were 20 with emphysema, 70 with heart problems and 30 with cancer for a total of 120. Under smoker there were 60 with emphysema, 80 with hear problems and 40 with cancer for a total of 180. The totals for emphysema were 80, for heart problems 150 and for cancer 70 and a grand total of 300 in the study We are interested in determining whether or not illness is independent of smoking.Conduct the appropriate test at an alpha level of 0.05 Columns are Illness–Nonsmoker–Smoker–Totals and the rows are the three illnesses and a total row.

# Hypothesis testing problems

A sample of n=9 scores is obtained from a normal population distribution with o-=12. The sample mean is M=60.

a- with a two-tailed test and o=.05,use the sample data to test the hypothesis that the population mean is u=65.

b- with a two-tailed test and o=.05, use the ample data to test the hypothesis that the population mean is u=55.

c- In parts (a) and (b) of this problem, you should find the u=65 and the u=55 are both acceptable hypotheses. Explain how two different values can both be acceptable.

# Hypothesis testing problems

Last year the records of Dairy Land Inc., a convenience store chain, showed the mean amount spent by a customer was \$30. A sample of 40 transactions this month revealed the mean amount spent was \$33 with a standard deviation of \$12. At the 0.05 significance level, can we conclude that the mean amount spent has increased? What is the p-value? Follow the five-step hypothesis testing procedure.

# Hypothesis testing problems :

A sample of 64 observations is selected from a normal population. The sample mean is 215, and the sample standard deviation is 15. Conduct the following test of hypothesis using the .03 significance level.

H0: µ &#8805; 220
H1: µ < 220

(a) Is this a one- or two-tailed test?
(b) What is the decision rule?
(c) What is the value of the test statistic?
(d) What is the p-value? Interpret it.
(e) What is your decision regarding H0?

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