Question: a) A study of n = 20 subjects retains the null hypothesis Ho: \(\mu \) = 170 at \(\alpha \) = 0.05 (two-sided). What vas the power of the test to identify a population mean of 190 if it is known that the population standard deviation \(\sigma \) = 40.

b) How large a sample is needed for a z-test with 90% power and \(\alpha \) = 0.05 (two-sided). It is known that the population standard deviation ( \(\sigma \) ) is 40. The null hypothesis assumes that \(\mu \) = 170 and the alternative hypothesis assumes that \(\mu \) =190.