Statistics / Applied Statistics and Probability for Engineers 6 / Chapter 9.11 / Problem 149SE

Applied Statistics and Probability for Engineers | 6th Edition | ISBN: 9781118539712 | Authors: Douglas C. Montgomery, George C. Runger

Ch 9.11 - 149SE

Chapter 9, Problem 149SE

(choose chapter or problem)

Suppose that you are testing $H_{0\ }:\ p=0.5$ versus $H_{0\ }:\ p\ne 0.5$. Suppose that $p$ is the true value of the population proportion.
(a) Using $\alpha=0.05$, 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 $\alpha=0.01$, 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 $\alpha{}$ on the power of the test for different sample sizes.
(c) Using $\alpha=0.05$, 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 $\alpha$ level.
(d) Using $\alpha=0.01$, what sample size is required if $p=0.6$ and we want $\beta=0.05$? What sample is required if $p=0.8$ and we want $\beta=0.05$? Compare the two sample sizes and comment on the effect of the true value of $p$ on a sample size required when $\beta$ is held approximately constant.