Chapter 4, Problem 10E

Using the data from Exercise 4.7, construct a 95% lower confidence interval on mean battery life. Why would the manufacturer be interested in a one-sided confidence interval?

4.7. The inside diameters of bearings used in an aircraft landing gear assembly are known to have a standard deviation of $\sigma =0.002\text{cm}\text{.}$ A random sample of 15 bearings has an average inside diameter of 8.2535 cm.

1. (a) Test the hypothesis that the mean inside bearing diameter is 8.25 cm. Use a two-sided alternative and $\alpha =\mathrm{0.05.}$
2. (b) Find the P-value for this test.
3. (c) Construct a 95% two-sided confidence interval on the mean bearing diameter.