Abearing used in an automotive application is required 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 α=0.01. the true mean hole diameter significantly different from 1.5 in. at α=0.01.

(b) what is the p-value for the test in part (a)? p-value = round your answer to two decimal places (e. g. 98.76).

(c) compute the power of the test if the true mean diameter is 1.495 inches. power of the test = round your answer to two decimal places (e. g. 98.76).

(d) 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 0.91? bearings