What are some weak points in this study relative to evaluating the potential of the

a. Place a 99 confidence interval on the average number of miles driven, m, prior to

the tires wearing out. b. Is there significant evidence a ⫽ .01 that the manufacturer’s claim is false? What is the level of significance of your test? Interpret your findings. 5.42 Refer to Exercise 5.41. Using the Minitab output given, compare your results to the results given by the computer program. a. Does the normality assumption appear to be valid? b. How close to the true value were your bounds on the p-value?

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

reached by your test of the hypotheses? Env. 5.43 The amount of sewage and industrial pollutants dumped into a body of water affects the health of the water by reducing the amount of dissolved oxygen available for aquatic life. Over a 2-month period, 8 samples were taken from a river at a location 1 mile downstream from a sewage treatment plant. The amount of dissolved oxygen in the samples was determined and is reported in the following table. The current research asserts that the mean dissolved oxygen level must be at least 5.0 parts per million ppm for fish to survive. Sample 1 2 3 4 5 6 7 8 n s Oxygen ppm 5.1 4.9 5.6 4.2 4.8 4.5 5.3 5.2 8 4.95 .45 a. Place a 95 confidence on the mean dissolved oxygen level during the 2-month period. b. Using the confidence interval from a, does the mean oxygen level appear to be less than 5 ppm?

c. Test the research hypothesis that the mean oxygen level is less than 5 ppm. What is

the level of significance of your test? Interpret your findings. Env. 5.44 A dealer in recycled paper places empty trailers at various sites. The trailers are gradually filled by individuals who bring in old newspapers and magazines, and are picked up on several schedules. One such schedule involves pickup every second week. This schedule is desirable if the average amount of recycled paper is more than 1,600 cubic feet per 2-week period. The dealer’s records for eighteen 2-week periods show the following volumes in cubic feet at a particular site: 1,660 1,820 1,590 1,440 1,730 1,680 1,750 1,720 1,900 1,570 1,700 1,900 1,800 1,770 2,010 1,580 1,620 1,690 ⫽ 1,718.3 and s ⫽ 137.8

a. Assuming the eighteen 2-week periods are fairly typical of the volumes throughout

the year, is there significant evidence that the average volume m is greater than 1,600 cubic feet? y y 40 35 30 25 Mil e s Boxplot of tire data Test of normality for tire data .999 .99 .95 .80 .50 .20 .05 .01 .001 Probability

25 30

35 40 Miles Test of mu ⫽ 35.00 vs mu ⬍ 35.00 Var iable N Mean StDev SE Mean T P 99.0 CI Miles 15 31.47 5.04 1.30 ⫺2.71 0.0084 27.59, 35.3 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