A tire company has developed a new tread design. To determine if the newly designed tire(Cont)

A tire company has developed a new tread design. To determine if the newly designed tire has a mean life of 60,000 miles or more, a random sample of 16 prototype tires is tested. The mean tire life for this sample is 60,758 miles. Assume that the tire life is normally distributed with unknown mean µ and standard deviation σ = 1500 miles. Test the hypothesis H0: µ = 60,000 vs. H1: µ greater than 60,000.
(a) Compute the test statistic and its P-value. Based on the P-value, state whether Ho can be rejected at α = 0.01.
(b) What is the power of the 0.01-level test in (a) if the true mean life for the new tread design is 61,000 miles?
(c) Suppose that at least 90% power is needed to identify a tread design that has the mean life of 61,000 miles. How many tires should be tested?