# You may need to use the approp

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A professor at a local university noted that the grades of her students were normally distributed with a mean of 79 and a standard deviation of 10. (Round your answers to one decimal place.)
(a)
The professor has informed us that 16.6 percent of her students received grades of A. What is the minimum score needed to receive a grade of A?

(b)
If 12.1 percent of her students failed the course and received F’s, what was the maximum score among those who received an F?

(c)
If 33 percent of the students received grades of B or better (i.e., A’s and B’s), what is the minimum score of those who received a B?

# You may need to use the approp

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An agency reports that 11.5% of workers in a particular country belonged to unions. Suppose a sample of 300 workers is collected to determine whether union efforts to organize have increased union membership.
(a)
Formulate the hypotheses that can be used to determine whether union membership has increased.
H0: p = 0.115
Ha: p ≠ 0.115
H0: p > 0.115
Ha: p ≤ 0.115

H0: p ≤ 0.115
Ha: p > 0.115
H0: p ≥ 0.115
Ha: p < 0.115
H0: p < 0.115
Ha: p ≥ 0.115
(b)
If the sample results show that 42 of the workers belonged to unions, what is the p-value for your hypothesis test?
Find the value of the test statistic. (Round your answer to two decimal places.)

p-value =
(c)
At

? = 0.05,

– Reject H0. There is sufficient evidence to conclude that there has been an increase in union membership.
– Do not reject H0. There is sufficient evidence to conclude that there has been an increase in union membership.
– Reject H0. There is insufficient evidence to conclude that there has been an increase in union membership.
– Do not reject H0. There is insufficient evidence to conclude that there has been an increase in union membership.

# You may need to use the approp

You may need to use the appropriate appendix table or technology to answer this question.
An agency reports that 11.7% of workers in a particular country belonged to unions. Suppose a sample of 300 workers is collected to determine whether union efforts to organize have increased union membership.
(a)
Formulate the hypotheses that can be used to determine whether union membership has increased.
H0: p = 0.117
Ha: p ≠ 0.117
H0: p ≥ 0.117
Ha: p < 0.117

H0: p ≤ 0.117
Ha: p > 0.117
H0: p < 0.117
Ha: p ≥ 0.117
H0: p > 0.117
Ha: p ≤ 0.117
(b)
If the sample results show that 42 of the workers belonged to unions, what is the p-value for your hypothesis test?
Find the value of the test statistic. (Round your answer to two decimal places.)

p-value =

# You may need to use the approp

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Fowle Marketing Research, Inc., bases charges to a client on the assumption that telephone surveys can be completed in a mean time of 13 minutes or less. If a longer mean survey time is necessary, a premium rate is charged. A sample of 35 surveys from a particular client provided the survey times shown in the file named Fowle. Based upon past studies, the population standard deviation is assumed known with

σ = 9 minutes.

Is the premium rate justified for this client?

 17 11 12 23 20 23 15 16 23 22 18 23 25 14 12 12 20 18 12 19 11 11 20 21 11 18 14 13 13 19 16 10 22 18 23
(a)
Formulate the null and alternative hypotheses for this application.
H0: μ > 13
Ha: μ ≤ 13
H0: μ = 13
Ha: μ ≠ 13

H0: μ ≤ 13
Ha: μ > 13
H0: μ < 13
Ha: μ ≥ 13
H0: μ ≥ 13
Ha: μ < 13
(b)
Compute the value of the test statistic. (Round your answer to two decimal places.)

(c)
p-value =
(d)
At

? = 0.01,

Do not reject H0. There is sufficient evidence to conclude that the premium rate should be charged.Reject H0. There is insufficient evidence to conclude that the premium rate should be charged.    Do not reject H0. There is insufficient evidence to conclude that the premium rate should be charged.Reject H0. There is sufficient evidence to conclude that the premium rate should be charged.

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Individuals filing federal income tax returns prior to March 31 received an average refund of \$1,057. Consider the population of “last-minute” filers who mail their tax return during the last five days of the income tax period (typically April 10 to April 15).
For a sample of 400 individuals who filed a tax return between April 10 and 15, the sample mean refund was \$910. Based on prior experience, a population standard deviation of

σ = \$1,600

may be assumed.

What is the test statistic? (Round your answer to two decimal places.)

p-value =

Find the value of the test statistic. (Round your answer to two decimal places.)

State the critical values for the rejection rule. (Use ? = 0.05. Round your answer to two decimal places. If the test is one-tailed, enter NONE for the unused tail.)
test statistic≤test statistic≥

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A manufacturer is well known for its high-quality die-cast metal alloy toy replicas of tractors and other farm equipment. As part of a periodic procurement evaluation, the manufacturer is considering purchasing parts for a toy tractor line from three different suppliers. The parts received from the suppliers are classified as having a minor defect, having a major defect, or being good. Test results from samples of parts received from each of the three suppliers are shown below. Note that any test with these data is no longer a test of proportions for the three supplier populations because the categorical response variable has three outcomes: minor defect, major defect, and good.
Part Tested Supplier
A B C
Minor Defect 16 14 22
Major Defect 4 10 4
Good 130 126 124
Using the data above, conduct a hypothesis test to determine if the distribution of defects is the same for the three suppliers. Use the chi-square test calculations as presented in this section with the exception that a table with r rows and c columns results in a chi-square test statistic with (r − 1)(c − 1) degrees of freedom.

Find the value of the test statistic. (Round your answer to three decimal places.)

p-value =

# You may need to use the approp

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A travel association reported the domestic airfare (in dollars) for business travel for the current year and the previous year. Below is a sample of 12 flights with their domestic airfares shown for both years.
Current
Year
Previous
Year
345 315
526 475
420 474
216 206
285 263
405 432
635 585
710 650
605 545
517 547
570 496
610 580
(a)
Formulate the hypotheses and test for a significant increase in the mean domestic airfare for business travel for the one-year period.
H0: μd ≥ 0
Ha: μd < 0
H0: μd ≤ 0
Ha: μd > 0

H0: μd ≠ 0
Ha: μd = 0
H0: μd < 0
Ha: μd = 0
H0: μd = 0
Ha: μd ≠ 0
Calculate the test statistic. (Use current year airfare − previous year airfare. Round your answer to three decimal places.)

p-value =
Using a 0.05 level of significance, what is your conclusion?
Reject H0. We can conclude that there has been a significant increase in the mean domestic airfare for business travel for the one-year period.Reject H0. We cannot conclude that there has been a significant increase in the mean domestic airfare for business travel for the one-year period.    Do not reject H0. We can conclude that there has been a significant increase in the mean domestic airfare for business travel for the one-year period.Do not reject H0. We cannot conclude that there has been a significant increase in the mean domestic airfare for business travel for the one-year period.
(b)
What is the sample mean domestic airfare (in dollars) for business travel for each year?
current\$ previous\$
(c)
What is the percentage change in mean airfare for the one-year period? (Round your answer to one decimal place.)
%

# You may need to use the approp

QUESTION 10

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In 2017, a website reported that only 10% of surplus food is being recovered in the food-service and restaurant sector, leaving approximately 1.5 billion meals per year uneaten. Assume this is the true population proportion and that you plan to take a sample survey of 565 companies in the food service and restaurant sector to further investigate their behavior.
(a)
Show the sampling distribution of

p,

the proportion of food recovered by your sample respondents.

A bell-shaped curve is above a horizontal axis labeled p.
• The curve enters the viewing window near -0.03 just above the horizontal axis, curves up to the right, and reaches a maximum near 0.01.
• The curve then curves down and to the right until it leaves the viewing window at the same height it entered near 0.05.

A bell-shaped curve is above a horizontal axis labeled p.
• The curve enters the viewing window near -2.9 just above the horizontal axis, curves up to the right, and reaches a maximum near 0.1.
• The curve then curves down and to the right until it leaves the viewing window at the same height it entered near 3.1.

A bell-shaped curve is above a horizontal axis labeled p.
• The curve enters the viewing window near -0.04 just above the horizontal axis, curves up to the right, and reaches a maximum near 0.00.
• The curve then curves down and to the right until it leaves the viewing window at the same height it entered near 0.04.

A bell-shaped curve is above a horizontal axis labeled p.
• The curve enters the viewing window near 0.06 just above the horizontal axis, curves up to the right, and reaches a maximum near 0.10.
• The curve then curves down and to the right until it leaves the viewing window at the same height it entered near 0.14.
(b)
What is the probability that your survey will provide a sample proportion within ±0.03 of the population proportion? (Round your answer to four decimal places.)

(c)
What is the probability that your survey will provide a sample proportion within ±0.015 of the population proportion? (Round your answer to four decimal places.)

# You may need to use the approp

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The following results come from two independent random samples taken of two populations.
Sample 1 Sample 2
n1 = 60
n2 = 35
x1 = 13.6
x2 = 11.6
?1 = 2.5
?2 = 3
(a)
What is the point estimate of the difference between the two population means? (Use

x1 − x2.)

(b)
Provide a 90% confidence interval for the difference between the two population means. (Use

x1 − x2.

to
(c)
Provide a 95% confidence interval for the difference between the two population means. (Use

x1 − x2.

to

# You may need to use the approp

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Suppose the mean price for used cars is \$10,198. A manager of a Kansas City used car dealership reviewed a sample of 50 recent used car sales at the dealership in an attempt to determine whether the population mean price for used cars at this particular dealership differed from the national mean. The prices for the sample of 50 cars are shown in the file named UsedCars.
 12,400 10,400 12,100 10,000 11,000 8,895 7,675 9,975 6,350 10,470 9,895 11,250 8,795 12,500 9,340 10,150 9,200 9,395 11,000 10,640 10,000 7,500 8,000 10,440 10,200 10,300 9,740 9,280 10,930 8,000 9,000 7,680 9,400 10,730 7,350 12,240 11,970 8,240 9,910 10,080 9,440 8,970 9,500 10,050 10,130 11,400 8,500 7,500 9,090 10,500
(a)
Formulate the hypotheses that can be used to determine whether a difference exists in the mean price for used cars at the dealership.
H0: μ ≤ 10,198
Ha: μ > 10,198
H0: μ = 10,198
Ha: μ ≠ 10,198

H0: μ ≥ 10,198
Ha: μ < 10,198
H0: μ > 10,198
Ha: μ ≤ 10,198
H0: μ < 10,198
Ha: μ ≥ 10,198
(b)
What is the test statistic? (Round your answer to three decimal places.)

p-value =

# You may need to use the approp

QUESTION 7

You may need to use the appropriate appendix table or technology to answer this question.
Assume a binomial probability distribution has

p = 0.60

and

n = 200.
(a)
What are the mean and standard deviation? (Round your answers to two decimal places.)
meanstandard deviation
(b)
Is this situation one in which binomial probabilities can be approximated by the normal probability distribution? Explain.
No, because np ≥ 5 and n(1 − p) ≥ 5.No, because np < 5 and n(1 − p) < 5.    Yes, because np < 5 and n(1 − p) < 5.Yes, because np ≥ 5 and n(1 − p) ≥ 5.Yes, because n ≥ 30.
(c)
What is the probability of 100 to 110 successes? Use the normal approximation of the binomial distribution to answer this question. (Round your answer to four decimal places.)

(d)
What is the probability of 130 or more successes? Use the normal approximation of the binomial distribution to answer this question. (Round your answer to four decimal places.)

(e)
What is the advantage of using the normal probability distribution to approximate the binomial probabilities?
The advantage would be that using the normal probability distribution to approximate the binomial probabilities makes the calculations less accurate.The advantage would be that using the normal probability distribution to approximate the binomial probabilities makes the calculations more accurate.    The advantage would be that using the normal probability distribution to approximate the binomial probabilities increases the number of calculations.The advantage would be that using the the normal probability distribution to approximate the binomial probabilities reduces the number of calculations.
How would you calculate the probability in part (d) using the binomial distribution. (Use f(x) to denote the binomial probability function.)
P(x ≥ 130) = f(130) + f(131) + f(132) + f(133) +    + f(200)
P(x ≥ 130) = f(0) + f(1) +    + f(128) + f(129)

P(x ≥ 130) = f(131) + f(132) + f(133) + f(134) +    + f(200)
P(x ≥ 130) = 1 − f(129) − f(130) − f(131) − f(132) −    − f(200)
P(x ≥ 130) = f(0) + f(1) +    + f(129) + f(130)

# You may need to use the approp

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Males in the Netherlands are the tallest, on average, in the world with an average height of 183 centimeters (cm).† Assume that the height of men in the Netherlands is normally distributed with a mean of 183 cm and standard deviation of 10.5 cm.
(a)
What is the probability that a Dutch male is shorter than 177 cm? (Round your answer to four decimal places.)

(b)
What is the probability that a Dutch male is taller than 196 cm? (Round your answer to four decimal places.)

(c)
What is the probability that a Dutch male is between 175 and 191 cm? (Round your answer to four decimal places.)

(d)
Out of a random sample of 1,000 Dutch men, how many would we expect to be taller than 188 cm? (Round your answer to the nearest integer.)
men

# You may need to use the approp

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The United States ranks ninth in the world in per capita chocolate consumption; Forbes reports that the average American eats 9.5 pounds of chocolate annually. Suppose you are curious whether chocolate consumption is higher in Hershey, Pennsylvania, the location of the Hershey Company’s corporate headquarters. A sample of 35 individuals from the Hershey area showed a sample mean annual consumption of 10.05 pounds and a standard deviation of s = 1.5 pounds. Using ? = 0.05, do the sample results support the conclusion that mean annual consumption of chocolate is higher in Hershey than it is throughout the United States?
State the null and alternative hypotheses. (Enter != for ≠ as needed.)
H0:

Ha:

Find the value of the test statistic. (Round your answer to three decimal places.)

p-value =

# You may need to use the approp

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Market-share-analysis company Net Applications monitors and reports on internet browser usage. According to Net Applications, in the summer of 2014, Google’s Chrome browser exceeded a 20% market share for the first time, with a 20.37% share of the browser market.† For a randomly selected group of 15 Internet browser users, answer the following questions. (Round your answers to four decimal places.)
(a)
Compute the probability that exactly 8 of the 15 Internet browser users use Chrome as their Internet browser. (Round your answer to four decimal places.)

(b)
Compute the probability that at least 3 of the 15 Internet browser users use Chrome as their Internet browser. (Round your answer to four decimal places.)

(c)
For the sample of 15 Internet browser users, compute the expected number of Chrome users.

(d)
For the sample of 15 Internet browser users, compute the variance and standard deviation for the number of Chrome users. (Round your answers to four decimal places.)
variancestandard deviation

# You may need to use the approp

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A magazine reports that women trust recommendations from a particular social networking site more than recommendations from any other social network platform. But does trust in this social networking site differ by gender? The following sample data show the number of women and men who stated in a recent sample that they trust recommendations made on this particular social networking site.
Women Men
Sample 150 170
Trust Recommendations
Made on the social networking site
123 102
(a)
What is the point estimate of the proportion of women who trust recommendations made on this particular social networking site?

(b)
What is the point estimate of the proportion of men who trust recommendations made on this particular social networking site?

(c)
Provide a 95% confidence interval estimate of the difference between the proportion of women and men who trust recommendations made on this particular social networking site. (Round your answers to four decimal places.)
to

# You may need to use the approp

You may need to use the appropriate appendix table or technology to answer this question.
Consider the following hypothesis test.
H0: p ≥ 0.75
Ha: p < 0.75
A sample of 270 items was selected. Compute the p-value and state your conclusion for each of the following sample results. Use

? = 0.05.
(a)
p = 0.68
Find the value of the test statistic. (Round your answer to two decimal places.)

p-value =
Do not reject H0. There is sufficient evidence to conclude that p < 0.75.Reject H0. There is sufficient evidence to conclude that p < 0.75.    Do not reject H0. There is insufficient evidence to conclude that p < 0.75.Reject H0. There is insufficient evidence to conclude that p < 0.75.
(b)
p = 0.71
Find the value of the test statistic. (Round your answer to two decimal places.)

p-value =
Do not reject H0. There is sufficient evidence to conclude that p < 0.75.Reject H0. There is sufficient evidence to conclude that p < 0.75.    Do not reject H0. There is insufficient evidence to conclude that p < 0.75.Reject H0. There is insufficient evidence to conclude that p < 0.75.
(c)
p = 0.70
Find the value of the test statistic. (Round your answer to two decimal places.)

p-value =
Do not reject H0. There is sufficient evidence to conclude that p < 0.75.Reject H0. There is sufficient evidence to conclude that p < 0.75.    Do not reject H0. There is insufficient evidence to conclude that p < 0.75.Reject H0. There is insufficient evidence to conclude that p < 0.75.
(d)
p = 0.77
Find the value of the test statistic. (Round your answer to two decimal places.)

p-value =

# You may need to use the approp

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Given that z is a standard normal random variable, find z for each situation. (Round your answers to two decimal places.)
(a)
The area to the left of z is 0.2420.

(b)
The area between −z and z is 0.9232.

(c)
The area between −z and z is 0.2128.

(d)
The area to the left of z is 0.9948.

(e)
The area to the right of z is 0.6554.

# You may need to use the approp

You may need to use the appropriate appendix table or technology to answer this question.
A simple random sample with

n = 56

provided a sample mean of 26.5 and a sample standard deviation of 4.4. (Round your answers to one decimal place.)

(a)
Develop a 90% confidence interval for the population mean.
to
(b)
Develop a 95% confidence interval for the population mean.
to
(c)
Develop a 99% confidence interval for the population mean.
to
(d)
What happens to the margin of error and the confidence interval as the confidence level is increased?
As the confidence level increases, there is a smaller margin of error and a more narrow confidence interval.As the confidence level increases, there is a smaller margin of error and a wider confidence interval.    As the confidence level increases, there is a larger margin of error and a wider confidence interval.As the confidence level increases, there is a larger margin of error and a more narrow confidence interval.

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Consider the following hypothesis test.
H0: μ = 100
Ha: μ ≠ 100
A sample of 65 is used. Identify the p-value and state your conclusion for each of the following sample results. Use

? = 0.05.
(a)
x = 103 and s = 11.5
Find the value of the test statistic. (Round your answer to three decimal places.)

p-value =
Do not reject H0. There is sufficient evidence to conclude that μ ≠ 100.Do not reject H0. There is insufficient evidence to conclude that μ ≠ 100.    Reject H0. There is sufficient evidence to conclude that μ ≠ 100.Reject H0. There is insufficient evidence to conclude that μ ≠ 100.
(b)
x = 96.5 and s = 11.0
Find the value of the test statistic. (Round your answer to three decimal places.)

p-value =
Do not reject H0. There is sufficient evidence to conclude that μ ≠ 100.Do not reject H0. There is insufficient evidence to conclude that μ ≠ 100.    Reject H0. There is sufficient evidence to conclude that μ ≠ 100.Reject H0. There is insufficient evidence to conclude that μ ≠ 100.
(c)
x = 102 and s = 10.5
Find the value of the test statistic. (Round your answer to three decimal places.)

p-value =

# You may need to use the approp

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A study showed that 62% of supermarket shoppers believe supermarket brands to be as good as national name brands. To investigate whether this result applies to its own product, the manufacturer of a national name-brand ketchup asked a sample of shoppers whether they believed that supermarket ketchup was as good as the national brand ketchup.
(a)
Formulate the hypotheses that could be used to determine whether the percentage of supermarket shoppers who believe that the supermarket ketchup was as good as the national brand ketchup is less than 62%.
H0: p = 0.62
Ha: p ≠ 0.62
H0: p ≥ 0.62
Ha: p < 0.62

H0: p < 0.62
Ha: p ≥ 0.62
H0: p > 0.62
Ha: p ≤ 0.62
H0: p ≤ 0.62
Ha: p > 0.62
(b)
If a sample of 100 shoppers showed 51 stating that the supermarket brand was as good as the national brand, what is the p-value?
Find the value of the test statistic. (Round your answer to two decimal places.)

# You may need to use the approp

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Barron’s reported that the average number of weeks an individual is unemployed is 18.5 weeks. Assume that for the population of all unemployed individuals the population mean length of unemployment is 18.5 weeks and that the population standard deviation is 6 weeks. Suppose you would like to select a sample of 50 unemployed individuals for a follow-up study.
(a)
Show the sampling distribution of

x,

the sample mean average for a sample of 50 unemployed individuals.

A bell-shaped curve is above a horizontal axis labeled weeks.
• The curve enters the viewing window near -2.4 just above the horizontal axis, curves up to the right, and reaches a maximum near 0.
• The curve then curves down and to the right until it leaves the viewing window at the same height it entered near 2.4.

A bell-shaped curve is above a horizontal axis labeled weeks.
• The curve enters the viewing window near 16.1 just above the horizontal axis, curves up to the right, and reaches a maximum near 18.5.
• The curve then curves down and to the right until it leaves the viewing window at the same height it entered near 20.9.

A bell-shaped curve is above a horizontal axis labeled weeks.
• The curve enters the viewing window near 0.5 just above the horizontal axis, curves up to the right, and reaches a maximum near 18.5.
• The curve then curves down and to the right until it leaves the viewing window at the same height it entered near 36.5.

A bell-shaped curve is above a horizontal axis labeled weeks.
• The curve enters the viewing window near 47.6 just above the horizontal axis, curves up to the right, and reaches a maximum near 50.
• The curve then curves down and to the right until it leaves the viewing window at the same height it entered near 52.4.
(b)
What is the probability that a simple random sample of 50 unemployed individuals will provide a sample mean within 1 week of the population mean? (Round your answer to four decimal places.)

(c)
What is the probability that a simple random sample of 50 unemployed individuals will provide a sample mean within

 1 2

week

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QUESTION 12

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After deducting grants based on need, the average cost to attend the University of Southern California (USC) is \$27,175. Assume the population standard deviation is \$7,400. Suppose that a random sample of 51 USC students will be taken from this population.
(a)
What is the value of the standard error of the mean? (Round your answer to the nearest whole number.)
(b)
What is the probability that the sample mean will be more than \$27,175?

(c)
What is the probability that the sample mean will be within \$1,000 of the population mean? (Round your answer to four decimal places.)

(d)
What is the probability that the sample mean will be within \$1,000 of the population mean if the sample size were increased to 100? (Round your answer to four decimal places.)

# You may need to use the approp

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Older people often have a hard time finding work. AARP reported on the number of weeks it takes a worker aged 55 plus to find a job. The data on number of weeks spent searching for a job contained in the file JobSearch are consistent with the AARP findings.
 21 14 51 16 17 14 16 12 48 0 27 17 32 24 12 10 52 21 26 14 13 24 19 28 26 26 10 21 44 36 22 39 17 17 10 19 16 22 5 22
(a)
Provide a point estimate of the population mean number of weeks it takes a worker aged 55 plus to find a job.
weeks
(b)
At 95% confidence, what is the margin of error? (Round your answer to four decimal places.)
weeks
(c)
What is the 95% confidence interval estimate of the mean? (Round your answers to two decimal places.)
weeks to  weeks
(d)
Discuss the degree of skewness found in the sample data. What suggestion would you make for a repeat of this study?
A histogram of the data shows the distribution is perfectly symmetric. One might suggest collecting a larger sample, at least 50, in the future.A histogram of the data shows some evidence that the distribution may be skewed to the right. One might suggest collecting a larger sample, at least 50, in the future.    A histogram of the data shows the distribution is perfectly symmetric. One might suggest collecting a smaller sample, at most 15, in the future.A histogram of the data shows some evidence that the distribution may be skewed to the right. One might suggest collecting a smaller sample, at most 15, in the future.

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QUESTION 11

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Airline passengers arrive randomly and independently at the passenger-screening facility at a major international airport. The mean arrival rate is 10 passengers per minute. (Round your answers to six decimal places.)
(a)
Compute the probability of no arrivals in a one-minute period.

(b)
Compute the probability that three or fewer passengers arrive in a one-minute period.

(c)
Compute the probability of no arrivals in a 15-second period.

(d)
Compute the probability of at least one arrival in a 15-second period.

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QUESTION 8

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A population proportion is 0.50. A sample of size 100 will be taken and the sample proportion

p

will be used to estimate the population proportion. (Round your answers to four decimal places.)

(a)
What is the probability that the sample proportion will be within ±0.03 of the population proportion?

(b)
What is the probability that the sample proportion will be within ±0.05 of the population proportion?

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IQ scores as measured by both the Stanford-Binet intelligence test and the Wechsler intelligence test have a mean of 100. The standard deviation for the Stanford-Binet test is 16, while that for the Wechsler test is 15. For which test do a smaller percentage of test-takers score less than 80?
WechslerStanford-Binet
Why?
Since this test has a smaller standard deviation, a greater percentage of scores fall within 20 points of the mean.

Since this test has a greater standard deviation, a smaller percentage of scores fall within 20 points of the mean.

Since this test has a greater standard deviation, a greater percentage of scores fall within 20 points of the mean.

Since this test has a smaller standard deviation, a smaller percentage of scores fall within 20 points of the mean.None of the above.

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Many small restaurants in Portland, Oregon, and other cities across the United States do not take reservations. Owners say that with smaller capacity, no-shows are costly, and they would rather have their staff focused on customer service rather than maintaining a reservation system.† However, it is important to be able to give reasonable estimates of waiting time when customers arrive and put their name on the waiting list. The file RestaurantLine contains 10 observations of number of people in line ahead of a customer (independent variable x) and actual waiting time (in minutes) (dependent variable y). The estimated regression equation is:

ŷ = 4.35 + 8.81x

and MSE = 94.42.

 Number of Customers Waiting Time (Minutes) 5 47 2 27 4 36 4 44 6 52 3 21 7 82 3 43 8 69 4 28

(a)
Develop a point estimate (in min) for a customer who arrives with five people on the wait-list. (Round your answer to two decimal places.)
ŷ* =  min
(b)
Develop a 95% confidence interval for the mean waiting time (in min) for a customer who arrives with five customers already in line. (Round your answers to two decimal places.)
min to  min
(c)
Develop a 95% prediction interval for Roger and Sherry Davy’s waiting time (in min) if there are five customers in line when they arrive. (Round your answers to two decimal places.)
min to  min
(d)
Discuss the difference between part (b) and part (c).
The prediction interval is much  —Select— narrower wider than the confidence interval. This is because it is  —Select— less more difficult to predict the waiting time for an individual customer arriving with five people in line than it is to estimate the mean waiting time for a customer arriving with five people in line.

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Suppose an institution categorizes colleges and universities on the basis of their research and degree-granting activities. Universities that grant doctoral degrees are placed into one of three classifications: moderate research activity, higher research activity, or highest research activity. The classifications for public and not-for-profit private doctoral degree-granting universities are summarized in the following table.
Type of
University
Classification
Moderate
Research
Activity
Higher
Research
Activity
Highest
Research
Activity
Public 28 71 96
Private 48 26 49
Test the hypothesis that the population proportions of public universities are equal in each classification category. Use a 0.05 level of significance. Find the value of the test statistic. (Round your answer to two decimal places.)

p-value =

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A report states that adults 18- to 24- years-old send and receive 128 texts every day. Suppose we take a sample of 25- to 34- year-olds to see if their mean number of daily texts differs from the mean for 18- to 24- year-olds.
(a)
State the null and alternative hypotheses we should use to test whether the population mean daily number of texts for 25- to 34-year-olds differs from the population daily mean number of texts for 18- to 24-year-olds. (Enter != for ≠ as needed.)
H0:
M=

Ha:
M=

Repeat the preceding hypothesis test using the critical value approach.
State the null and alternative hypotheses. (Enter != for ≠ as needed.)
H0:
M=

Ha:
M=

Find the value of the test statistic. (Round your answer to two decimal places.)

State the critical values for the rejection rule. (Use ? = 0.05. Round your answer to two decimal places. If the test is one-tailed, enter NONE for the unused tail.)
test statistic≤ test statistic≥

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The sample data below represent the number of late and on time flights for three airlines.
Airline
Flight 1 2 3
Late 15 27 32
On Time 285 273 368
(a)
Formulate the hypotheses for a test that will determine if the population proportion of late flights is the same for all three airlines.
H0p1 = p2 = p3
Ha: All population proportions are not equal.H0: All population proportions are not equal.
Hap1 = p2 = p3    H0: Not all population proportions are equal.
Hap1 = p2 = p3H0p1 = p2 = p3
Ha: Not all population proportions are equal.

(b)
Conduct the hypothesis test with a 0.05 level of significance.

Find the value of the test statistic. (Round your answer to three decimal places.)

p-value =

c) Compute the sample proportion of late flights for each airline.
p1=
p2=
p3 =

What is the overall proportion of late flights for the three airlines?
p=

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number 27

You may need to use the appropriate appendix table or technology to answer this question.
The life expectancy of a certain country is 79 with a standard deviation of 6 years. A random sample of 64 individuals is selected. (Round your answers to four decimal places.)
(a)
What is the probability that the sample mean will be larger than 81 years?

(b)
What is the probability that the sample mean will be less than 77.5 years?

(c)
What is the probability that the sample mean will be between 77 and 82 years?

(d)
What is the probability that the sample mean will be between 76 and 78 years?

(e)
What is the probability that the sample mean will be larger than 77 years?

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A magazine conducts an annual survey in which readers rate their favorite cruise ship. All ships are rated on a 100-point scale, with higher values indicating better service. A sample of 33 ships that carry fewer than 500 passengers resulted in an average rating of 85.16, and a sample of 44 ships that carry 500 or more passengers provided an average rating of 81.90. Assume that the population standard deviation is 4.55 for ships that carry fewer than 500 passengers and 3.97 for ships that carry 500 or more passengers.
(a)
What is the point estimate of the difference between the population mean rating for ships that carry fewer than 500 passengers and the population mean rating for ships that carry 500 or more passengers? (Use smaller cruise ships − larger cruise ships.)

(b)
At 95% confidence, what is the margin of error? (Round your answer to two decimal places.)

(c)
What is a 95% confidence interval estimate of the difference between the population mean ratings for the two sizes of ships? (Use smaller cruise ships − larger cruise ships. Round your answers to two decimal places.)
to

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A Deloitte employment survey asked a sample of human resource executives how their company planned to change its workforce over the next 12 months. A categorical response variable showed three options: the company plans to hire and add to the number of employees, the company plans no change in the number of employees, or the company plans to lay off and reduce the number of employees. Another categorical variable indicated if the company was private or public. Sample data for 180 companies are summarized as follows.
Employment Plan Company
Private Public
No Change 19 34
Lay Off Employees 16 42
(a)
Conduct a test of independence to determine if the employment plan for the next 12 months is independent of the type of company.
State the null and alternative hypotheses.
H0: Employment plan is not mutually exclusive from the type of company.
Ha: Employment plan is mutually exclusive from the type of company.H0: Employment plan is mutually exclusive from the type of company.
Ha: Employment plan is not mutually exclusive from the type of company.    H0: Employment plan is not independent of the type of company.
Ha: Employment plan is independent of the type of company.H0: Employment plan is independent of the type of company.
Ha: Employment plan is not independent of the type of company.

Find the value of the test statistic. (Round your answer to three decimal places.)

p-value =

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QUESTION 7

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The state of California has a mean annual rainfall of 22 inches, whereas the state of New York has a mean annual rainfall of 42 inches. Assume that the standard deviation for both states is 4 inches. A sample of 33 years of rainfall for California and a sample of 46 years of rainfall for New York has been taken.
(a)
Show the probability distribution of the sample mean annual rainfall for California.
A bell-shaped curve is above a horizontal axis labeled inches.
• The curve enters the viewing window near 10 just above the horizontal axis, curves up to the right, and reaches a maximum near 22.
• The curve then curves down and to the right until it leaves the viewing window at the same height it entered near 34.

A bell-shaped curve is above a horizontal axis labeled inches.
• The curve enters the viewing window near 39.9 just above the horizontal axis, curves up to the right, and reaches a maximum near 42.
• The curve then curves down and to the right until it leaves the viewing window at the same height it entered near 44.1.

A bell-shaped curve is above a horizontal axis labeled inches.
• The curve enters the viewing window near 19.9 just above the horizontal axis, curves up to the right, and reaches a maximum near 22.
• The curve then curves down and to the right until it leaves the viewing window at the same height it entered near 24.1.

A bell-shaped curve is above a horizontal axis labeled inches.
• The curve enters the viewing window near −2.1 just above the horizontal axis, curves up to the right, and reaches a maximum near 0.
• The curve then curves down and to the right until it leaves the viewing window at the same height it entered near 2.1.
(b)
What is the probability that the sample mean is within 1 inch of the population mean for California? (Round your answer to four decimal places.)

(c)
What is the probability that the sample mean is within 1 inch of the population mean for New York? (Round your answer to four decimal places.)

(d)
In which case, part (b) or part (c), is the probability of obtaining a sample mean within 1 inch of the population mean greater? Why?
part (c), because the population standard deviation is smallerpart (c), because the sample size is larger    part (b), because the population standard deviation is smallerpart (b), because the standard error is smaller

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Suppose a company surveyed the work preferences and attitudes of 1,006 working adults spread over three generations: baby boomers, Generation X, and millennials. In one question, individuals were asked if they would leave their current job to make more money at another job. The sample data are summarized in the following table.
Leave Job for
More Money?
Generation
Baby Boomer Generation X Millennial
Yes 124 154 167
No 202 185 174
Conduct a test of independence to determine whether interest in leaving a current job for more money is independent of employee generation.
State the null and alternative hypotheses.
H0: Interest in leaving job for more money is not independent of the employee generation.
Ha: Interest in leaving job for more money is independent of the employee generation.H0: Interest in leaving job for more money is not mutually exclusive of the employee generation.
Ha: Interest in leaving job for more money is mutually exclusive of the employee generation.    H0: Interest in leaving job for more money is independent of the employee generation.
Ha: Interest in leaving job for more money is not independent of the employee generation.H0: Interest in leaving job for more money is mutually exclusive of the employee generation.
Ha: Interest in leaving job for more money is not mutually exclusive of the employee generation.

Find the value of the test statistic. (Round your answer to two decimal places.)

# You may need to use the approp

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Consider the following hypothesis test.
H0: ?1 − ?2 = 0
Ha: ?1 − ?2 ≠ 0
The following results are from independent samples taken from two populations.
Sample 1 Sample 2
n1 = 35
n2 = 40
x1 = 13.6
x2 = 10.1
s1 = 5.8
s2 = 8.7
(a)
What is the value of the test statistic? (Use

x1 − x2.

(b)
What is the degrees of freedom for the t distribution? (Round your answer down to the nearest integer.)

(c)
p-value =
(d)
At

? = 0.05,

Do not Reject H0. There is sufficient evidence to conclude that ?1 − ?2 ≠ 0.Reject H0. There is sufficient evidence to conclude that ?1 − ?2 ≠ 0.     Do not Reject H0. There is insufficient evidence to conclude that ?1 − ?2 ≠ 0.Reject H0. There is insufficient evidence to conclude that ?1 − ?2 ≠ 0.

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The average return for large-cap domestic stock funds over three years was 14.4%. Assume the three-year returns were normally distributed across funds with a standard deviation of 4.4%.
(a)
What is the probability an individual large-cap domestic stock fund had a three-year return of at least 23%? (Round your answer to four decimal places.)

(b)
What is the probability an individual large-cap domestic stock fund had a three-year return of 10% or less? (Round your answer to four decimal places.)

(c)
How big does the return have to be to put a domestic stock fund in the top 15% for the three-year period? (Round your answer to two decimal places.)

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According to a research center, 21% of all merchandise sold in a particular country gets returned. A department store in a certain city sampled 80 items sold in January and found that 28 of the items were returned.
(a)
Construct a point estimate of the proportion of items returned for the population of sales transactions at the store in the given city.

(b)
Construct a 95% confidence interval for the proportion of returns at the store in the given city. (Round your answers to four decimal places.)
to
(c)
Is the proportion of returns at the store in the given city significantly different from the returns for the country as a whole? Provide statistical support for your answer.
Develop appropriate hypotheses such that rejection of H0 will support the conclusion that the proportion of returns at the store in the given city is significantly different from the returns for the country as a whole.
H0: p ≥ 0.21
Ha: p < 0.21
H0: p = 0.21
Ha: p ≠ 0.21

H0: p ≤ 0.21
Ha: p > 0.21
H0: p > 0.21
Ha: p ≤ 0.21
H0: p < 0.21
Ha: p ≥ 0.21
Find the value of the test statistic. (Round your answer to two decimal places.)

p-value =
At

? = 0.01,

Do not reject H0. There is insufficient evidence to conclude that the return rate for the store in the given city is different than the country’s national return rate.Reject H0. There is insufficient evidence to conclude that the return rate for the store in the given city is different than the country’s national return rate.    Reject H0. There is sufficient evidence to conclude that the return rate for the store in the given city is different than the country’s national return rate.Do not reject H0. There is sufficient evidence to conclude that the return rate for the store in the given city is different than the country’s national return rate.

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The increasing annual cost (including tuition, room, board, books, and fees) to attend college has been widely discussed (Time.com). The following random samples show the annual cost of attending private and public colleges. Data are in thousands of dollars.
Private Colleges

 52.8 44.2 45 33.3 44 29.6 45.8 37.8 49.5 43

Public Colleges

 20.3 22 28.2 15.6 24.1 28.5 22.8 25.8 18.5 25.6 14.4 21.8
(a)
Compute the sample mean (in thousand dollars) and sample standard deviation (in thousand dollars) for private colleges. (Round the standard deviation to two decimal places.)
sample mean\$   thousandsample standard deviation\$   thousand
Compute the sample mean (in thousand dollars) and sample standard deviation (in thousand dollars) for public colleges. (Round the standard deviation to two decimal places.)
sample mean\$   thousandsample standard deviation\$   thousand
(b)
What is the point estimate (in thousand dollars) of the difference between the two population means? (Use Private − Public.)
\$   thousand
Interpret this value in terms of the annual cost (in dollars) of attending private and public colleges.
We estimate that the mean annual cost to attend private colleges is \$   more than the mean annual cost to attend public college
(c)
Develop a 95% confidence interval (in thousand dollars) of the difference between the mean annual cost of attending private and public colleges. (Use Private − Public. Round your answers to one decimal place.)
\$   thousand to \$   thousand

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Carl Allen and Norm Nixon are two loan officers at a certain bank. The bank manager is interested in comparing the default rate on the loans approved by Carl to the default rate on the loans approved by Norm. In the sample of loans collected, there are 70 loans approved by Carl (14 of which defaulted) and 80 loans approved by Norm (9 of which defaulted).
(a)
State the hypothesis test that the default rates are the same for the two loan officers. (Let p1 = the population proportion of Carl’s loans that default, and let p2 = the population proportion of Norm’s loans that default. Enter != for ≠ as needed.)
H0:

Ha:

(b)
What is the sample default proportion for Carl?

What is the sample default proportion for Norm?

(c)
Use a 0.05 level of significance.
Calculate the test statistic. (Use

p1 − p2.

p-value =
Reject H0. We can conclude there is a significant difference between the population default proportions in the loans approved by Carl and the loans approved by Norm.Do not reject H0. We cannot conclude there is a significant difference between the population default proportions in the loans approved by Carl and the loans approved by Norm.    Do not reject H0. We can conclude there is a significant difference between the population default proportions in the loans approved by Carl and the loans approved by Norm.Reject H0. We cannot conclude there is a significant difference between the population default proportions in the loans approved by Carl and the loans approved by Norm.

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You may need to use the appropriate appendix table or technology to answer this question.
A simple random sample of 90 items resulted in a sample mean of 60. The population standard deviation is

σ = 15.
(a)
Compute the 95% confidence interval for the population mean. (Round your answers to two decimal places.)
to
(b)
Assume that the same sample mean was obtained from a sample of 180 items. Provide a 95% confidence interval for the population mean. (Round your answers to two decimal places.)
to
(c)
What is the effect of a larger sample size on the interval estimate?
A larger sample size provides a smaller margin of error.A larger sample size provides a larger margin of error.    A larger sample size does not change the margin of error.

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Consider the data.
 xi yi 1 2 3 4 5 4 7 5 10 14
Use the t test to test the following hypotheses (? = 0.05):
 H0: β1 = 0 Ha: β1 ≠ 0
Find the value of the test statistic. (Round your answer to three decimal places.)

p-value =

Use the F test to test the hypotheses in part (d) at a 0.05 level of significance. Present the results in the analysis of variance table format.
Set up the ANOVA table. (Round your values for MSE and F to two decimal places, and your p-value to three decimal places.)
Source
of Variation
Sum
of Squares
Degrees
of Freedom
Mean
Square
F p-value
Regression
Error
Total
Find the value of the test statistic. (Round your answer to two decimal places.)

p-value =

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Consider the following results for independent samples taken from two populations.
Sample 1 Sample 2
n1 = 400
n2 = 300
p1 = 0.53
p2 = 0.31
(a)
What is the point estimate of the difference between the two population proportions? (Use

p1 − p2.

)

(b)
Develop a 90% confidence interval for the difference between the two population proportions. (Use

p1 − p2.

to
(c)
Develop a 95% confidence interval for the difference between the two population proportions. (Use

p1 − p2.

to

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You may need to use the appropriate appendix table to answer this question.
According to Money magazine, Maryland had the highest median annual household income of any state in 2018 at \$75,847.† Assume that annual household income in Maryland follows a normal distribution with a median of \$75,847 and standard deviation of \$33,800.
(a)
What is the probability that a household in Maryland has an annual income of \$110,000 or more? (Round your answer to four decimal places.)

(b)
What is the probability that a household in Maryland has an annual income of \$50,000 or less? (Round your answer to four decimal places.)

(c)
What is the probability that a household in Maryland has an annual income between \$60,000 and \$70,000? (Round your answer to four decimal places.)

(d)
What is the annual income (in \$) of a household in the ninety-first percentile of annual household income in Maryland? (Round your answer to the nearest cent.)

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In a large university, 45% of the students are female.
(a)
If a random sample of twenty students is selected, what is the probability that the sample contains exactly four female students? (Round your answer to four decimal places.)

(b)
If a random sample of twenty students is selected, what is the probability that the sample will contain exactly 15 female students? (Round your answer to four decimal places.)

(c)
If a random sample of twenty students is selected, what is the probability that the sample will contain exactly twenty female students? (Round your answer to four decimal places.)

(d)
If a random sample of twenty students is selected, what is the probability that the sample will contain more than nine female students? (Round your answer to four decimal places.)

(e)
If a random sample of twenty students is selected, what is the probability that the sample will contain fewer than five female students? (Round your answer to four decimal places.)

(f)
If a random sample of twenty students is selected, what is the expected number of female students?

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According to Money magazine, Maryland had the highest median annual household income of any state in 2018 at \$75,847.† Assume that annual household income in Maryland follows a normal distribution with a median of \$75,847 and standard deviation of \$33,800.
(a)
What is the probability that a household in Maryland has an annual income of \$90,000 or more? (Round your answer to four decimal places

What is the annual income (in \$) of a household in the ninety-first percentile of annual household income in Maryland? (Round your answer to the nearest cent

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11b.

You may need to use the appropriate appendix table or technology to answer this question.
Product filling weights are normally distributed with a mean of 450 grams and a standard deviation of 30 grams.

a, What happens when a Type II error is made?
– The process will be declared in control and allowed to continue when the process is actually out of control.
– The process will be declared out of control and adjusted when the process is actually in control.
b,
– What is the probability of a Type I error for a sample of size 10? (Round your answer to four decimal places.)

– What is the probability of a Type I error for a sample of size 20? (Round your answer to four decimal places.)

– What is the probability of a Type I error for a sample of size 30? (Round your answer to four decimal places.)

c, What is the advantage of increasing the sample size for control chart purposes? What error probability is reduced as the sample size is increased?
– Increasing the sample size provides a more accurate estimate of the process mean and reduces the probability of making a Type I error.
– Increasing the sample size always increases the likelihood that the process is in control and reduces the probability of making a Type II error.  –  Increasing the sample size always increases the likelihood that the process is in control and reduces the probability of making a Type I error.
– Increasing the sample size provides a more accurate estimate of the process mean and reduces the probability of making a Type II error.

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6, You may need to use the appropriate technology to answer this question.
A client wants to determine whether there is a significant difference in the time required to complete a program evaluation with the three different methods that are in common use. Suppose the times (in hours) required for each of 18 evaluators to conduct a program evaluation follow.
Method 1 Method 2 Method 3
69 63 59
71 74 65
67 77 68
76 69 55
75 73 58
73 70 63
a, Use ? = 0.05 and test to see whether there is a significant difference in the time required by the three methods.
State the null and alternative hypotheses.
– H0: All populations of times are identical.
Ha: Not all populations of times are identical.
– H0: Median1 = Median2 = Median3
Ha: Median1 > Median2 > Median3
–  H0: Not all populations of times are identical.
Ha: All populations of times are identical.
– H0: Median1 ≠ Median2 ≠ Median3
Ha: Median1 = Median2 = Median3
– H0: Median1 = Median2 = Median3
Ha: Median1 ≠ Median2 ≠ Median3
b, Find the value of the test statistic. (Round your answer to two decimal places.) and  the p-value. (Round your answer to three decimal places.)

– Reject H0. There is not sufficient evidence to conclude that there is a significant difference in the time required by the three methods.
– Do not reject H0. There is sufficient evidence to conclude that there is a significant difference in the time required by the three methods.
– Do not reject H0. There is not sufficient evidence to conclude that there is a significant difference in the time required by the three methods.
– Reject H0. There is sufficient evidence to conclude that there is a significant difference in the time required by the three methods.

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Consider the following hypothesis test.
H0: μ ≥ 55
Ha: μ < 55
A sample of 36 is used. Identify the p-value and state your conclusion for each of the following sample results. Use

? = 0.01.
(a)
x = 54 and s = 5.3
Find the value of the test statistic. (Round your answer to three decimal places.)

p-value =
Do not reject H0. There is insufficient evidence to conclude that μ < 55.Do not reject H0. There is sufficient evidence to conclude that μ < 55.    Reject H0. There is sufficient evidence to conclude that μ < 55.Reject H0. There is insufficient evidence to conclude that μ < 55.
(b)
x = 53 and s = 4.6
Find the value of the test statistic. (Round your answer to three decimal places.)

p-value =
Do not reject H0. There is insufficient evidence to conclude that μ < 55.Do not reject H0. There is sufficient evidence to conclude that μ < 55.    Reject H0. There is sufficient evidence to conclude that μ < 55.Reject H0. There is insufficient evidence to conclude that μ < 55.
(c)
x = 56 and s = 4.0
Find the value of the test statistic.

p-value =
Do not reject H0. There is insufficient evidence to conclude that μ < 55.Do not reject H0. There is sufficient evidence to conclude that μ < 55.    Reject H0. There is sufficient evidence to conclude that μ < 55.Reject H0. There is insufficient evidence to conclude that μ < 55.

# You may need to use the approp

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According to the Vivino website, suppose the mean price for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is \$32.48. A New England-based lifestyle magazine wants to determine if red wines of the same quality are less expensive in Providence, and it has collected prices for 65 randomly selected red wines of similar quality from wine stores throughout Providence. The mean and standard deviation for this sample are \$30.15 and \$12, respectively.
(a)
Develop appropriate hypotheses for a test to determine whether the sample data support the conclusion that the mean price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of \$32.48. (Enter != for ≠ as needed.)
H0:

Ha:

(b)
Using the sample from the 65 bottles, what is the test statistic? (Round your answer to three decimal places.)

Using the sample from the 65 bottles, what is the p-value? (Round your answer to four decimal places.)
p-value =
(c)
At ? = 0.05, what is your conclusion?
Do not reject H0. We cannot conclude that the price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of \$32.48.Do not reject H0. We can conclude that the price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of \$32.48.    Reject H0. We can conclude that the price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of \$32.48.Reject H0. We cannot conclude that the price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of \$32.48.
(d)
Repeat the preceding hypothesis test using the critical value approach.
State the null and alternative hypotheses. (Enter != for ≠ as needed.)
H0:

Ha:

Find the value of the test statistic. (Round your answer to three decimal places.)

State the critical values for the rejection rule. Use

? = 0.05.

(Round your answers to three decimal places. If the test is one-tailed, enter NONE for the unused tail.)

test statistic≤test statistic≥
Do not reject H0. We cannot conclude that the price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of \$32.48.Do not reject H0. We can conclude that the price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of \$32.48.    Reject H0. We can conclude that the price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of \$32.48.Reject H0. We cannot conclude that the price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of \$32.48.

# you may need to use the approp

you may need to use the appropriate appendix table or technology to answer this question.
The gap between the earnings of men and women with equal education is narrowing but has not closed. Sample data for seven men and seven women with bachelor’s degrees are as follows. Data are shown in thousands of dollars.
Men Women
30.6 42.5
86.5 46.4
56.2 31.9
68.2 40.5
45.2 36.8
57.9 51.5
66.3 22.8
(a)
What is the median salary (in \$) for men? For women?
men\$57900 women\$40500
(b)
Use ? = 0.05 and conduct the hypothesis test for identical population distributions.
State the null and alternative hypotheses.
H0: Median salary for men − Median salary for women > 0
Ha: Median salary for men − Median salary for women = 0H0: Median salary for men − Median salary for women ≤ 0
Ha: Median salary for men − Median salary for women > 0    H0: The two populations of salaries are not identical.
Ha: The two populations of salaries are identical.H0: Median salary for men − Median salary for women ≥ 0
Ha: Median salary for men − Median salary for women < 0H0: The two populations of salaries are identical.
Ha: The two populations of salaries are not identical.
Find the value of the test statistic.
W =
p-value =

# You may need to use the approp

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A consumer product testing organization uses a survey of readers to obtain customer satisfaction ratings for the nation’s largest supermarkets. Each survey respondent is asked to rate a specified supermarket based on a variety of factors such as: quality of products, selection, value, checkout efficiency, service, and store layout. An overall satisfaction score summarizes the rating for each respondent with 100 meaning the respondent is completely satisfied in terms of all factors. Suppose sample data representative of independent samples of two supermarkets’ customers are shown below.
Supermarket 1 Supermarket 2
n1 = 290
n2 = 300
x1 = 83
x2 = 82
(a)
Formulate the null and alternative hypotheses to test whether there is a difference between the population mean customer satisfaction scores for the two retailers. (Let ?1 = the population mean satisfaction score for Supermarket 1’s customers, and let ?2 = the population mean satisfaction score for Supermarket 2’s customers. Enter != for ≠ as needed.)
H0:

Ha:

(b)
Assume that experience with the satisfaction rating scale indicates that a population standard deviation of 14 is a reasonable assumption for both retailers. Conduct the hypothesis test.
Calculate the test statistic. (Use

?1 − ?2.

p-value =
At a 0.05 level of significance what is your conclusion?
Reject H0. There is sufficient evidence to conclude that the population mean satisfaction scores differ for the two retailers.Do not reject H0. There is not sufficient evidence to conclude that the population mean satisfaction scores differ for the two retailers.    Do not reject H0. There is sufficient evidence to conclude that the population mean satisfaction scores differ for the two retailers.Reject H0. There is not sufficient evidence to conclude that the population mean satisfaction scores differ for the two retailers.
(c)
Which retailer, if either, appears to have the greater customer satisfaction?
Supermarket 1Supermarket 2    neither
Provide a 95% confidence interval for the difference between the population mean customer satisfaction scores for the two retailers. (Use

x1 − x2.

to

# You may need to use the approp

You may need to use the appropriate technology to answer this question.
A travel association reported the domestic airfare (in dollars) for business travel for the current year and the previous year. Below is a sample of 12 flights with their domestic airfares shown for both years.
Current
Year
Previous
Year
345 315
526 451
420 474
216 206
285 275
405 432
635 585
710 650
605 545
517 547
570 496
610 580
(a)
Formulate the hypotheses and test for a significant increase in the mean domestic airfare for business travel for the one-year period.
H0: ?d = 0
Ha: ?d ≠ 0
H0: ?d < 0
Ha: ?d = 0

H0: ?d ≥ 0
Ha: ?d < 0
H0: ?d ≤ 0
Ha: ?d > 0
H0: ?d ≠ 0
Ha: ?d = 0
Calculate the test statistic. (Use current year airfare − previous year airfare. Round your answer to three decimal places.)

p-value =
Using a 0.05 level of significance, what is your conclusion?
Reject H0. We can conclude that there has been a significant increase in the mean domestic airfare for business travel for the one-year period. Do not reject H0. We can conclude that there has been a significant increase in the mean domestic airfare for business travel for the one-year period.     Reject H0. We cannot conclude that there has been a significant increase in the mean domestic airfare for business travel for the one-year period. Do not reject H0. We cannot conclude that there has been a significant increase in the mean domestic airfare for business travel for the one-year period.
(b)
What is the sample mean domestic airfare (in dollars) for business travel for each year?
current \$ previous \$
(c)
What is the percentage change in mean airfare for the one-year period? (Round your answer to one decimal place.)
%

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According to the Vivino website, suppose the mean price for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is \$32.48. A New England-based lifestyle magazine wants to determine if red wines of the same quality are less expensive in Providence, and it has collected prices for 65 randomly selected red wines of similar quality from wine stores throughout Providence. The mean and standard deviation for this sample are \$30.15 and \$12, respectively.
(a)
Develop appropriate hypotheses for a test to determine whether the sample data support the conclusion that the mean price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of \$32.48. (Enter != for ≠ as needed.)
H0:

Ha:

(b)
Using the sample from the 65 bottles, what is the test statistic? (Round your answer to three decimal places.)

Using the sample from the 65 bottles, what is the p-value? (Round your answer to four decimal places.)
p-value =
(c)
At ? = 0.05, what is your conclusion?
Do not reject H0. We cannot conclude that the price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of \$32.48.Do not reject H0. We can conclude that the price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of \$32.48.    Reject H0. We can conclude that the price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of \$32.48.Reject H0. We cannot conclude that the price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of \$32.48.
(d)
Repeat the preceding hypothesis test using the critical value approach.
State the null and alternative hypotheses. (Enter != for ≠ as needed.)
H0:

Ha:

Find the value of the test statistic. (Round your answer to three decimal places.)

State the critical values for the rejection rule. Use

? = 0.05.

(Round your answers to three decimal places. If the test is one-tailed, enter NONE for the unused tail.)

test statistic≤test statistic≥

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A magazine subscriber study asked, “In the past 12 months, when traveling for business, what type of airline ticket did you purchase most often?” A second question asked if the type of airline ticket purchased most often was for domestic or international travel. Sample data obtained are shown in the following table.
Type of Ticket Type of Flight
Domestic International
First class 29 22
Economy class 519 136

Using a 0.05 level of significance, is the type of ticket purchased independent of the type of flight?

Find the value of the test statistic. (Round your answer to three decimal places.)

p-value =

# You may need to use the approp

You may need to use the appropriate appendix table or technology to answer this question.
Money reports that the average annual cost of the first year of owning and caring for a large dog in 2017 is \$1,448. The Irish Red and White Setter Association of America has requested a study to estimate the annual first-year cost for owners of this breed. A sample of 50 will be used. Based on past studies, the population standard deviation is assumed known with

σ = \$230.
 1,902 2,042 1,936 1,817 1,504 1,572 1,532 1,907 1,882 2,153 1,945 1,335 2,006 1,516 1,839 1,739 1,456 1,958 1,934 2,094 1,739 1,434 1,667 1,679 1,736 1,670 1,770 2,052 1,379 1,939 1,854 1,913 2,163 1,737 1,888 1,737 2,230 2,131 1,813 2,118 1,978 2,166 1,482 1,700 1,679 2,060 1,683 1,850 2,232 2,294
(a)
What is the margin of error for a 95% confidence interval of the mean cost in dollars of the first year of owning and caring for this breed? (Round your answer to nearest cent.)
\$
(b)
The DATAfile Setters contains data collected from fifty owners of Irish Setters on the cost of the first year of owning and caring for their dogs. Use this data set to compute the sample mean. Using this sample, what is the 95% confidence interval for the mean cost in dollars of the first year of owning and caring for an Irish Red and White Setter? (Round your answers to nearest cent.)
\$_______ to \$________

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According to statistics reported on news source, a surprising number of motor vehicles are not covered by insurance. Sample results, consistent with the news report, showed 72 of 400 vehicles were not covered by insurance.
(a)
What is the point estimate of the proportion of vehicles not covered by insurance?

(b)
Develop a 95% confidence interval for the population proportion. (Round your answer to four decimal places.)
to

# You may need to use the approp

You may need to use the appropriate appendix table to answer this question. The average return for large-cap domestic stock funds over three years was 14.4%. Assume the three-year returns were normally distributed across funds with a standard deviation of 4.4%. (a) What is the probability an individual large-cap domestic stock fund had a three-year return of at least 19%? (Round your answer to four decimal places.) (b) What is the probability an individual large-cap domestic stock fund had a three-year return of 10% or less? (Round your answer to four decimal places.) (c) How big does the return have to be to put a domestic stock fund in the top 15% for the three-year period? (Round your answer to two decimal places.)

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QUESTION 12

You may need to use the appropriate appendix table or technology to answer this question.
A group conducted a survey of 13,000 brides and grooms married in the United States and found that the average cost of a wedding is \$28,858. Assume that the cost of a wedding is normally distributed with a mean of \$28,858 and a standard deviation of \$5,400.
(a)
What is the probability that a wedding costs less than \$18,000? (Round your answer to four decimal places.)

(b)
What is the probability that a wedding costs between \$18,000 and \$32,000? (Round your answer to four decimal places.)

(c)
What is the minimum cost (in dollars) for a wedding to be included among the most expensive 5% of weddings? (Round your answer to the nearest dollar.)

# You may need to use the approp

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Phone calls arrive at the rate of 48 per hour at the reservation desk for Regional Airways. (Round your answers to four decimal places.)
(a)
Compute the probability of receiving three calls in a 5-minute interval of time.

(b)
Compute the probability of receiving exactly 10 calls in 15 minutes.

(c)
Suppose no calls are currently on hold. If the agent takes 5 minutes to complete the current call, how many callers do you expect to be waiting by that time?

What is the probability that none will be waiting?

(d)
If no calls are currently being processed, what is the probability that the agent can take 3 minutes for personal time without being interrupted by a call?

# You may need to use the approp

You may need to use the appropriate appendix table or technology to answer this question.
Consider a binomial experiment with

n = 10

and

p = 0.30.
(a)
Compute

f(0).

f(0) =
(b)
Compute

f(2).

f(2) =
(c)
Compute

P(x ≤ 2).

P(x ≤ 2) =
(d)
Compute

P(x ≥ 1).

P(x ≥ 1) =
(e)
Compute

E(x).
E(x) =
(f)
Compute

Var(x)

Var(x)

=σ=

# You may need to use the approp

QUESTION 11

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Alexa is the popular virtual assistant developed by Amazon. Alexa interacts with users using artificial intelligence and voice recognition. It can be used to perform daily tasks such as making to-do lists, reporting the news and weather, and interacting with other smart devices in the home. In 2018, the Amazon Alexa app was downloaded some 2,800 times per day from the Google Play store.† Assume that the number of downloads per day of the Amazon Alexa app is normally distributed with a mean of 2,800 and standard deviation of 860.
(a)
What is the probability there are 2,100 or fewer downloads of Amazon Alexa in a day? (Round your answer to four decimal places.)

(b)
What is the probability there are between 1,400 and 2,600 downloads of Amazon Alexa in a day? (Round your answer to four decimal places.)

(c)
What is the probability there are more than 3,100 downloads of Amazon Alexa in a day? (Round your answer to four decimal places.)

(d)
Suppose that Google has designed its servers so there is probability 0.03 that the number of Amazon Alexa app downloads in a day exceeds the servers’ capacity and more servers have to be brought online. How many Amazon Alexa app downloads per day are Google’s servers designed to handle? (Round your answer to the nearest integer.)

# You may need to use the approp

You may need to use the appropriate technology to answer this question.
A survey was conducted to determine whether hours of sleep per night are independent of age. A sample of individuals was asked to indicate the number of hours of sleep per night with categorical options: fewer than 6 hours, 6 to 6.9 hours, 7 to 7.9 hours, and 8 hours or more. Later in the survey, the individuals were asked to indicate their age with categorical options: age 39 or younger and age 40 or older. Sample data follow.
Hours of Sleep Age Group
39 or younger 40 or older
Fewer than 6 38 36
6 to 6.9 60 57
7 to 7.9 77 75
8 or more 65 92
(a)
Conduct a test of independence to determine whether hours of sleep are independent of age.
State the null and alternative hypotheses.
H0: Hours of sleep per night is mutually exclusive from age.
Ha: Hours of sleep per night is not mutually exclusive from age.H0: Hours of sleep per night is independent of age.
Ha: Hours of sleep per night is not independent of age.    H0: The proportion of people who get 8 or more hours of sleep per night is not equal across the two age groups.
Ha: The proportion of people who get 8 or more hours of sleep per night is equal across the two age groups.H0: Hours of sleep per night is not independent of age.
Ha: Hours of sleep per night is independent of age.

Find the value of the test statistic. (Round your answer to three decimal places.)

p-value =

What is your estimate of the percentages of individuals who sleep fewer than 6 hours, 6 to 6.9 hours, 7 to 7.9 hours, and 8 hours or more per night?
Fewer than 6  :              %
6 to 6.9  :                        %
7 to 7.9   :                       %
8 or more    :                  %

# You may need to use the approp

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Suppose a company surveyed the work preferences and attitudes of 1,006 working adults spread over three generations: baby boomers, Generation X, and millennials. In one question, individuals were asked if they would leave their current job to make more money at another job. The sample data are summarized in the following table.
Leave Job for
More Money?
Generation
Baby Boomer Generation X Millennial
Yes 124 155 166
No 202 186 173

Find the value of the test statistic. (Round your answer to two decimal places.)

# You may need to use the approp

You may need to use the appropriate appendix table or technology to answer this question.
An agency reports that 11.5% of workers in a particular country belonged to unions. Suppose a sample of 300 workers is collected to determine whether union efforts to organize have increased union membership.
(a)
Formulate the hypotheses that can be used to determine whether union membership has increased.
H0: p = 0.115
Ha: p ≠ 0.115
H0: p > 0.115
Ha: p ≤ 0.115

H0: p ≤ 0.115
Ha: p > 0.115
H0: p ≥ 0.115
Ha: p < 0.115
H0: p < 0.115
Ha: p ≥ 0.115
(b)
If the sample results show that 36 of the workers belonged to unions, what is the p-value for your hypothesis test?
Find the value of the test statistic. (Round your answer to two decimal places.)

p-value =
(c)
At

? = 0.05,

Do not reject H0. There is insufficient evidence to conclude that there has been an increase in union membership.Reject H0. There is sufficient evidence to conclude that there has been an increase in union membership.    Do not reject H0. There is sufficient evidence to conclude that there has been an increase in union membership.Reject H0. There is insufficient evidence to conclude that there has been an increase in union membership.

# You may need to use the approp

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The time needed to complete a final examination in a particular college course is normally distributed with a mean of 100 minutes and a standard deviation of 20 minutes. Answer the following questions.
(a)
What is the probability of completing the exam in one hour or less?
(b)
What is the probability that a student will complete the exam in more than 60 minutes but less than 65 minutes?
(c)
Assume that the class has 90 students and that the examination period is 130 minutes in length. How many students do you expect will be unable to complete the exam in the allotted time?

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A Deloitte employment survey asked a sample of human resource executives how their company planned to change its workforce over the next 12 months. A categorical response variable showed three options: the company plans to hire and add to the number of employees, the company plans no change in the number of employees, or the company plans to lay off and reduce the number of employees. Another categorical variable indicated if the company was private or public. Sample data for 180 companies are summarized as follows.
Employment Plan Company
Private Public
No Change 19 34
Lay Off Employees 16 42

Conduct a test of independence to determine if the employment plan for the next 12 months is independent of the type of company.

Find the value of the test statistic. (Round your answer to three decimal places.)

p-value =

# You may need to use the approp

QUESTION 4

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Given that z is a standard normal random variable, find z for each situation. (Round your answers to two decimal places.)
(a)
The area to the left of z is 0.9750.

(b)
The area between 0 and z is 0.4750.

(c)
The area to the left of z is 0.7357.

(d)
The area to the right of z is 0.1314.

(e)
The area to the left of z is 0.8106.

(f)
The area to the right of z is 0.1894.

# You may need to use the approp

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Suppose that the mean daily viewing time of television is 8.35 hours. Use a normal probability distribution with a standard deviation of 2.5 hours to answer the following questions about daily television viewing per household

(a)
What is the probability that a household views television between 5 and 11 hours a day? (Round your answer to four decimal places.)

(b)
How many hours of television viewing must a household have in order to be in the top 4% of all television viewing households? (Round your answer to two decimal places.)
hrs

(c)
What is the probability that a household views television more than 4 hours a day? (Round your answer to four decimal places.)

# You may need to use the approp

You may need to use the appropriate appendix table or technology to answer this question.
According to the Vivino website, suppose the mean price for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is \$32.48. A New England-based lifestyle magazine wants to determine if red wines of the same quality are less expensive in Providence, and it has collected prices for 65 randomly selected red wines of similar quality from wine stores throughout Providence. The mean and standard deviation for this sample are \$30.15 and \$12, respectively.

(d)
Repeat the preceding hypothesis test using the critical value approach.
State the null and alternative hypotheses. (Enter != for ≠ as needed.)
H0:

Ha:

Find the value of the test statistic. (Round your answer to three decimal places.)

State the critical values for the rejection rule. Use

? = 0.05.

(Round your answers to three decimal places. If the test is one-tailed, enter NONE for the unused tail.)

test statistic≤test statistic≥

# You may need to use the approp

You may need to use the appropriate appendix table or technology to answer this question.
A consumer product testing organization uses a survey of readers to obtain customer satisfaction ratings for the nation’s largest supermarkets. Each survey respondent is asked to rate a specified supermarket based on a variety of factors such as: quality of products, selection, value, checkout efficiency, service, and store layout. An overall satisfaction score summarizes the rating for each respondent with 100 meaning the respondent is completely satisfied in terms of all factors. Suppose sample data representative of independent samples of two supermarkets’ customers are shown below.
Supermarket 1 Supermarket 2
n1 = 290
n2 = 300
x1 = 82
x2 = 81
(a)
Formulate the null and alternative hypotheses to test whether there is a difference between the population mean customer satisfaction scores for the two retailers. (Let μ1 = the population mean satisfaction score for Supermarket 1’s customers, and let μ2 = the population mean satisfaction score for Supermarket 2’s customers. Enter != for ≠ as needed.)
H0:

Ha:

(b)
Assume that experience with the satisfaction rating scale indicates that a population standard deviation of 17 is a reasonable assumption for both retailers. Conduct the hypothesis test.
Calculate the test statistic. (Use

μ1 − μ2.

p-value =
At a 0.05 level of significance what is your conclusion?
Do not reject H0. There is sufficient evidence to conclude that the population mean satisfaction scores differ for the two retailers. Do not reject H0. There is not sufficient evidence to conclude that the population mean satisfaction scores differ for the two retailers.     Reject H0. There is sufficient evidence to conclude that the population mean satisfaction scores differ for the two retailers. Reject H0. There is not sufficient evidence to conclude that the population mean satisfaction scores differ for the two retailers.
(c)
Which retailer, if either, appears to have the greater customer satisfaction?
Supermarket 1 Supermarket 2     neither
Provide a 95% confidence interval for the difference between the population mean customer satisfaction scores for the two retailers. (Use

x1 − x2.

to

# You may need to use the approp

You may need to use the appropriate appendix table or technology to answer this question.
Recall the method used to obtain a confidence interval for the difference between two population means for matched samples.
(a)
The following data are from matched samples taken from two populations. Compute the difference value for each element. (Use Population 1 − Population 2.)
Element Population Difference
1 2
1 11 8
2 7 8
3 9 6
4 12 7
5 13 10
6 15 15
7 15 14
(b)
Compute

d.

(c)
Compute the standard deviation

sd.

(d)
What is the point estimate of the difference between the two population means? (Use Population 1 − Population 2.)

(e)
Provide a 95% confidence interval for the difference between the two population means. (Use Population 1 − Population 2. Round your answers to two decimal places.)
to

# You may need to use the approp

You may need to use the appropriate appendix table or technology to answer this question.
Consider the following data for two independent random samples taken from two normal populations.
 Sample 1 Sample 2 10 7 13 7 9 8 8 7 8 4 6 9
(a)
Compute the two sample means.
Sample 1Sample 2
(b)
Compute the two sample standard deviations. (Round your answers to two decimal places.)
Sample 1Sample 2
(c)
What is the point estimate of the difference between the two population means? (Use Sample 1 − Sample 2.)

(d)
What is the 90% confidence interval estimate of the difference between the two population means? (Use Sample 1 − Sample 2. Round your answers to two decimal places.)
to

# You may need to use the approp

You may need to use the appropriate appendix table or technology to answer this question.
Consider the following hypothesis test.
H0: p = 0.20
Ha: p ≠ 0.20
A sample of 500 provided a sample proportion

p = 0.175.
(a)
Compute the value of the test statistic. (Round your answer to two decimal places.)

(b)
p-value =
(c)
At

? = 0.05,

Reject H0. There is sufficient evidence to conclude that p ≠ 0.20.Do not reject H0. There is sufficient evidence to conclude that p ≠ 0.20.    Reject H0. There is insufficient evidence to conclude that p ≠ 0.20.Do not reject H0. There is insufficient evidence to conclude that p ≠ 0.20.
(d)
What is the rejection rule using the critical value? (Round your answer to two decimal places. If the test is one-tailed, enter NONE for the unused tail.)
test statistic≤test statistic≥

# You may need to use the approp

You may need to use the appropriate appendix table or technology to answer this question.
Consider the following hypothesis test.
H0: μ1 − μ2 ≤ 0
Ha: μ1 − μ2 > 0
The following results are for two independent samples taken from the two populations.
Sample 1 Sample 2
n1 = 40
n2 = 50
x1 = 25.7
x2 = 22.8
σ1 = 5.8
σ2 = 6
(a)
What is the value of the test statistic? (Round your answer to two decimal places.)

(b)

(c)
With

? = 0.05,

what is your hypothesis testing conclusion?

Reject H0. There is sufficient evidence to conclude that μ1 − μ2 > 0.Reject H0. There is insufficient evidence to conclude that μ1 − μ2 > 0.     Do not reject H0. There is insufficient evidence to conclude that μ1 − μ2 > 0.Do not Reject H0. There is sufficient evidence to conclude that μ1 − μ2 > 0.

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