A tire company claims that the lifetimes of its tires average 50,000 miles. The standard deviation of tire lifetimes is known to be 5,000 miles. You sample 100 tires and will test the hypothesis that the mean tire lifetime is at least 50,000 miles against the alternative that it is less. Assume, in fact, that the true mean lifetime is 49,500 miles.
(a) State the null and alternate hypotheses. Which hypothesis is true?
(A) H0: µ ≥ 50,000 versus H1: µ > 50,000. H1 is true, since the true value of µ is 49,500.
(B) H0: µ = 50,000 versus H1: µ ≠ 50,000. H1 is true, since the true value of µ is 49,500.
(C) H0: µ ≥ 50,000 versus H1: µ < 50,000. H1 is true, since the true value of µ is 49,500.
(b) It is decided to reject H0 if the sample mean is less than 49,400. Find the level of the test.
(c) Find the power of the test in part (b).