Ch 9.11 - 143SE

Chapter 9, Problem 143SE

(choose chapter or problem)

Suppose that we wish to test the hypothesis \(H_0\ :\ \mu=85\) versus the alternative \(H_{1\ }:\ \mu>85\) where \(\sigma=16\). Suppose that the true mean is \(\mu=86\) and that in the practical context of the problem, this is not a departure from  that has practical significance.
(a) For a test with \(\alpha=0.01\), compute \(\beta\) for the sample sizes \(n=25\), and 2500 assuming that \(\mu=86\).
(b) Suppose that the sample average is \(\bar{x}=86\). Find the -value for the test statistic for the different sample sizes specified in part (a). Would the data be statistically significant at \(\alpha=0.01\)?
(c) Comment on the use of a large sample size in this problem.

Equation Transcription:

Text Transcription:

H_0:mu=85

H_1:mu>85

sigma=16

mu=86

mu_0=85

alpha=0.01

beta

n=25

mu=86

x bar=86

alpha=0.01