A tire company claims that the lifetimes of its tires average 50750 miles. The standard deviation of tire lifetimes is known to be 5750 miles. You sample 175 tires and will test the hypothesis that the mean tire lifetime is at least 50750 miles against the alternative that it is less. Assume, in fact, that the true mean lifetime is 50250 miles. A) It is decided to reject H0 if the sample mean is less than 50150. Find the level and power of this test.
B) If the test is made at the 5% level, what is the power?
C) At what level should the test be conducted so that the power is 0.87?
D) You are given the opportunity to sample more tires. How many tires should be sampled in total so that the power is 0.87 if the test is made at the 5% level?