Chapter 8, Problem 8.100ACB

Durability of shock absorbers. A manufacturer of automobile shock absorbers was interested in comparing the durability of its shocks with that of the shocks produced by its biggest competitor. To make the comparison, one of the manufacturer’s and one of the competitor’s shocks were randomly selected and installed on the rear wheels of each of six cars. After the cars had been driven 20,000 miles, the strength of each test shock was measured, coded, and recorded. Results of the examination are shown in the table.

Car Number	Manufacturer’s Shock	Competitor’s Shock
1	8.8	8.4
2	10.5	10.1
3	12.5	12.0
4	9.7	9 3
5	9.6	9.0
6	13.2	13.0

1. a. Explain why the data are collected as matched pairs.
2. b. Do the data present sufficient evidence to conclude that there is a difference in the mean strength of the two types of shocks after 20,000 miles of use? Use α= .05.
3. c. Find the approximate observed significance level for the test and interpret its value.
4. d. What assumptions are necessary to apply a paired difference analysis to the data?
5. e. Construct a 95% confidence interval for μ_d. Interpret the confidence interval.
6. f. Suppose the data are based on independent random samples. Construct a 95% confidence interval for (μ₁ – μ₂). Interpret your result.
7. g. Compare the confidence intervals you obtained in parts e and f. Which is wider? To what do you attribute the difference in width? Assuming in each case that the appropriate assumptions are satisfied, which interval provides you with more information about (μ₁ – μ₂)? Explain.
8. h. Are the results of an unpaired analysis valid if the data come from a paired experiment?