Hypothesis testing and statist

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 Attitudestoward Tobacco Control Policies?Massachusetts, 1993-1995)
1993 1995
Adult Smoking Behavior
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 53*

* p < .05

Hypothesis Testing and Statist

You have been fortunate enough to receive a grant from a foundation studying pain in arthritis victims under the age of 30. You have not found a lot of people, but you think that you may have identified something that works pretty good. They are measured on an established scale pain scale from 20 (not much pain) to 100 (a lot of pain). You had already started treating them in two different ways before you realized, “Boy-howdy, I should have taken pain measurements at the beginning.” All you can do now is a measurement on both groups at the end of three months, but you can do that. Assuming that they all started with about the same scores, here’s the pain scores at the end for your six patients, three in each group.

Traditional Nontraditional
Heat/stretching acupuncture/deep massage/diet

45 34
50 29
38 41

a. Write null hypothesis for this research.
b. What is the level of measurement used in this research?
c. Are the two groups being measured the same or independent?
d. What inferential statistic would you recommend to determine if the difference between the two groups is significant?
e. Use another statistic and compare your answers.
f. Are the two groups significantly different from each other? (Show your work.)
g. Write a summary statement.

Hypothesis Testing and Statist

1. HO: µ = 70
H1: µ > 70
? = 20, n = 100, xbar = 80, ? = .01
a) calculate the value of the test statistic
b) set up the rejection region.
c) determine the p-value
d) interpret the results
attach file please

2. Draw the operating characteristic curve for n = 10, 50, and 100 for the following test:
Ho: ? = 400
Hi: ? > 400
? = .05, ? = 50
Attach file please

3. Determine the sample size necessary to estimate a population proportion to within .03 with 90% confidence assuming you have no knowledge of the approximate value of the sample proportion.

4. Some traffic experts believe that the major cause of highway collisions is the differing speeds of cars. That is, when some cars are driven slowly while others are driven at speeds well in excess of the speed limit, cars tend to congregate in bunches, increasing the probability of accidents. Thus, the greater the variation in speeds, the greater will be the number of collisions that occur. Suppose that one expert believes that when the variance exceeds 18 mph, the number of accidents will be unacceptably high. A random sample of the speeds of 245 cars on a highway with one of the highest accidents rates in the country is taken. Can we conclude at the 10% significance level that the variance in speeds exceeds 18 mph? Data is in file below.

5. How much time do executives spend each day reading and sending e-mail? A survey was conducted to obtain this information. The response (in minutes) in file below. Can we infer from these data that the mean amount of time spent reading and sending e-mail differs from 60 minutes each day? Data is in file below.

Hypothesis Testing and Statist

1. The owner of the Kate and Edith Cake Company state that the average number of buns sold daily was 1,500. A worker in the store wants to test the accuracy of the boss’s statement. A random sample of 36 days showed that the average daily sales were 1,450 buns. Using a level of significance of .01 and assuming that the standard deviation is 120, what should the worker conclude?

2. Mr. Tyrone Hops, the supervisor of the local brewery, wants to make sure that the average volume of the Super-Duper cans is 16 ounces. If the average volume is significantly less than 16 ounces, customers (and various agencies) would likely complain, prompting undesirable publicity. The physical size of the can does not allow an average volume significantly above 16 ounces. A random sample of 36 cans showed a sample mean of 15.7 ounces. Assuming that the standard deviation is 0.2 ounces, conduct a hypothesis test with the level of significance equal to .01.

3. Dr. I. M Sain, a psychologist, administered IQ tests to determine if female college students were as smart as male students. The sample of 40 females had a mean score of 131 with a standard deviation of 15. The sample of 36 males had a mean of 126 and a standard deviation of 17. At the .01 level of significance, is there a difference?

4. Discount Stores Corporation owns outlet A and outlet B. For the past year, outlet A has spent more dollars on advertising widgets than outlet B. The corporation wants to determine if the advertising has resulted in more sales for outlet A. A sample of 36 days at outlet A had a mean of 170 widgets sold daily. A sample of 36 days at outlet B had a mean of 165. Assuming that the variance of the first test is 36 and the variance of the second test is 25 respectfully, what would be concluded if a test were conducted at the .05 level of significance?

5. The following table reports the earnings per share (in dollars) for the Heban Lumber Mill from 1997 to 2003.

Year 1997 1998 1999 2000 2001 2002 2003
Earnings per share 1.56 1.86 2.17 2.41 2.67 2.97 3.40

a. Plot the data on a chart.
b. Estimate the linear trend equation by drawing a line through the data.
c. Determine the least squares trend equation.
d. Estimate the earnings per share for 2004.

6. A major oil company is studying the relationship between the daily traffic count and the number of gallons of gasoline pumped at company stations. A sample of eight company owned stations is selected and the following information obtained:

Location Total Gallons of Gas Pumped (000) Traffic Count of Vehicles (000)
West St. 120 4
Willouhby St. 180 6
Mallard Rd. 140 5
Pheasant Rd. 150 5
I-75 210 8
Kinzua Rd. 100 3
Front St. 90 3
Indiana Ave. 80 2

a. Develop a scatter diagram with the amount of gasoline pumped as the dependent variable.
b. Compute the coefficient of correlation
c. Compute the coefficient of determination.
d. Interpret the meaning of the coefficient of determination.
e. Test to determine whether the correlation in the population is zero, versus the alternate hypothesis that the correlation is greater than zero. Use the 0.05 significance level.

Hypothesis testing and statist

Please see the attached file.
9. Consider the following hypothesis test:
Ho:u > 20
Ho:u < 20
A sample of 50 provided a sample mean of 19.4. The population standard deviation is 2.
a. Compute the value of the test statistic.
b. What is the p-value?
c. Using a = .05, what is your conclusion?
d. What is the rejection rule using the critical value? What is your conclusion?

23. Consider the following hypothesis test:
Ho:u < 12
Ho:u > 12
A sample of 25 provided a sample mean xbar=14 and a sample standard deviation s = 4.32
a. Compute the value of the test statistic.
b. Use the t distribution table to compute a range for the p-value.
c. At a = .05, what is your conclusion?
d. What is the rejection rule using the critical value? What is your conclusion?

25. Consider the following hypothesis test:
Ho:u > 45
Ho:u < 45
A sample of 36 is used. Identify the p-value and state your conclusion for each of the following sample results. Use a = .01.
a. xbar = 44 and s = 5.2
b. xbar = 43 and s = 4.6
c. xbar = 46 and s = 5.0

29. The cost of a one-carat VS2 clarity, H color diamond from Diamond Source USA is $5600. A Midwestern jeweler makes calls to contacts in the diamond district of New York City to see whether the mean price of diamonds there differs from $5600.

a. Formulate hypotheses that can be use to determine whether the mean price in New York City differs from $5600.
b. There was a sample of 25 New York City contacts. What is the p-value?
c. At a = .05, can the null hypothesis be rejected? What is your conclusion?
d. Repeat the preceding hypothesis test using the critical value approach.

Ch. 18
1. A process that is in control has a mean of u = 12.5 and a standard deviation of o = .8
a. Construct an x chart if samples of size 4 are to be used.
b. Repeat part (a) for samples of size 8 and 16.
c. What happens to the limits of the control chart as the sample size is increased? Discuss why this change is reasonable.

3. Twenty-five samples of 100 items each were inspected when a process was considered to be operating satisfactorily. In the 25 samples, 135 items were found to be defective.
a. What is an estimate of the proportion defective when the process is in control?
b. What is the standard error of the proportion if sample sizes of size 100 will be used for statistical process control?
c. Compute the upper and lower limits for the control chart.

9. An automotive industry supplier produces pistons for several models of automobiles.
20 samples, each consisting of 200 pistons, were selected when the process was
known to be operating in conrol. The numbers of defective pistons found in the
samples follow.
8 10 6 4 5 7 8 12 8 15
14 10 10 7 5 8 6 10 4 8
a. What is an estimate of the proportion defective for the piston manufacturing process when it is in control?
b. Construct a p chart for the manufacturing process, assuming each sample has 200 pistons.
c. With the results of part (b), what conclusion should be drawn if a sample of 200 has 20 defective pistons?
d. Compute the upper and lower control limits for an np chart.
e. Answer part (c) using the results of part (d).