Suppose we are testing H0: p = 0.5 versus H0: p ( 0.5. Suppose that p is the true value of the population proportion.
(a) Using a = 0.05, find the power of the test for n = 100, 150, and 300 assuming that p = 0.6. Comment on the effect of sample size on the power of the test.
(b) Using a = 0.01, find the power of the test for n = 100, 150, and 300 assuming that p = 0.6. Compare your answers to those from part (a) and comment on the effect of a on the power of the test for different sample sizes.
(c) Using a = 0.05, find the power of the test for n = 100, assuming p  0.08. Compare your answer to part (a) and comment on the effect of the true value of p on the power of the test for the same sample size and a level.
(d) Using a = 0.01, what sample size is required if p = 0.6 and we want B = 0.05? What sample is required if p = 0.8 and we want B = 0.05? Compare the two sample sizes and comment on the effect of the true value of p on sample size required when B is held approximately constant.