A bearing used in an automotive application is suppose to have a nominal inside diameter of 1.5 inches. A random sample of 25 bearings is selected and the average inside diameter of these bearings is 1.4975 inches. Bearing diameter is known to be normally distributed with standard deviation σ = 0.01 inch.
(a) Test the hypotheses H0: μ = 1.5 versus H1: μ = 1.5 using a = 0.01.
(b) Compute the power of the test if the true mean diameter is 1.495 inches. (c) What sample size would be required to detect a true mean diameter as low as 1.495 inches if we wanted the power of the test to be at least 0.9?
(d) Explain how the question in part (a) could be answered by constructing a two-sided confidence interval on the mean diameter.