Is there a contradiction between the interval estimate of m and the conclusion

b. Place a 95 confidence interval on m. c. Compute the p-value for the test statistic. Is there strong evidence that m is greater than 1,600? Gov. 5.45 A federal regulatory agency is investigating an advertised claim that a certain device can increase the gasoline mileage of cars mpg. Ten such devices are purchased and installed in cars belonging to the agency. Gasoline mileage for each of the cars is recorded both before and after installation. The data are recorded here. Car 1 2 3 4 5 6 7 8 9 10 n s Before mpg 19.1 29.9 17.6 20.2 23.5 26.8 21.7 25.7 19.5 28.2 10 23.22 4.25 After mpg 25.8 23.7 28.7 25.4 32.8 19.2 29.6 22.3 25.7 20.1 10 25.33 4.25 Change mpg 6.7 ⫺ 6.2 11.1 5.2 9.3 ⫺ 7.6 7.9 ⫺ 3.4 6.2 ⫺ 8.1 10 2.11 7.54 Place 90 confidence intervals on the average mpg for both the before and after phases of the study. Interpret these intervals. Does it appear that the device will significantly increase the average mileage of cars? 5.46 Refer to Exercise 5.45. a. The cars in the study appear to have grossly different mileages before the devices were installed. Use the change data to test whether there has been a significant gain in mileage after the devices were installed. Use a ⫽ .05.

b. Construct a 90 confidence interval for the mean change in mileage. On the basis of

this interval, can one reject the hypothesis that the mean change is either zero or neg- ative? Note that the two-sided 90 confidence interval corresponds to a one-tailed a ⫽ .05 test by using the decision rule: reject H : m ⱖ m if m is greater than the upper limit of the confidence interval.

5.47 Refer to Exercise 5.45. a. Calculate the probability of a Type II error for several values of m

c , the average change in mileage. How do these values affect the conclusion you reached in Exercise 5.46?

b. Suggest some changes in the way in which this study in Exercise 5.45 was conducted.

5.8 Inferences about M When Population Is Nonnormal and n Is Small: Bootstrap Methods 5.48 Refer to Exercise 5.38.

a. Use a computer program to obtain 1,000 bootstrap samples from the 20 comprehen-

sion scores. Use these 1,000 samples to obtain the bootstrap p-value for the t test of H a : m ⬎ 80. b. Compare the p-value from part a to the p-value obtained in Exercise 5.39. 5.49 Refer to Exercise 5.41.

a. Use a computer program to obtain 1,000 bootstrap samples from the 15 tire wear

data. Use these 1,000 samples to obtain the bootstrap p-value for the t test of H a : m ⬍ 35. b. Compare the p-value from part a to the p-value obtained in Exercise 5.41. 5.50 Refer to Exercise 5.43.

a. Use a computer program to obtain 1,000 bootstrap samples from the 8 oxygen levels.

Use these 1,000 samples to obtain the bootstrap p-value for the t test of H a : m ⬍ 5. b. Compare the p-value from part a to the p-value obtained in Exercise 5.43. 5.51 Refer to Exercise 5.44.

a. Use a computer program to obtain 1,000 bootstrap samples from the 18 recycle vol-

umes. Use these 1,000 samples to obtain the bootstrap p-value for the t test of H a : m ⬎ 1,600.

b. Compare the p-value from part a to the p-value obtained in Exercise 5.44. x