A certain wastewater treatment method is supposed to

Chapter 6, Problem 7E

(choose chapter or problem)

A certain wastewater treatment method is supposed to neutralize the wastewater so that the mean pH is 7. Measurements of pH will be made on seven specimens of treated wastewater, and a test of the hypotheses \(H_{0}: \mu=7\) versus \(H_{1}: \mu \neq 7\) will be made using the Student’s t test (Section 6.4). Assume that the true mean is \(\mu=6.5\), the pH measurements are normally distributed with mean \(\mu\) and standard deviation 0.5, and the test is made at the 5% level.

a. Let \(X_{1}\), . . . , \(X_{7}\) denote the pH measurements, let \(\overline X\) denote their mean, and let s denote their sample standard deviation. What is the test statistic? For what values of the test statistic will \(H_{0}\) be rejected?

b. Generate 10,000 samples \(X_{1}^{*}\),....,\(X_{7}^{*}\) from the true distribution of pH measurements. For each sample, compute the test statistic and determine whether \(H_{0}\) is rejected. Estimate the power of the test.

Equation Transcription:

Text Transcription:

H_0:=7

H_1:7

mu=6.5

mu

X_1

X_7

overline{X}

H_0

X_1^*

X_7^*

H_0