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 Ho : H = 7 versus H1 : µ z 7 will be made using the Student's t test (Section 6.4). Assume that the true mean is u = 6.5, the pH measurements are normally distributed with mean µi and standard deviation 0.5, and the test is made at the 5% level. a. Let X1, .., X7 denote the pH measurements, let 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 Ho be rejected? b. Generate 10,000 samples X;.., X; from the true distribution of pH measurements. For each sample, compute the test statistic and determine whether Ho is rejected. Estimate the power of the test.

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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 Ho : H = 7 versus H1 : µ z 7 will be made using the Student's t
test (Section 6.4). Assume that the true mean is u = 6.5, the pH measurements are normally
distributed with mean µi and standard deviation 0.5, and the test is made at the 5% level.
a. Let X1, .., X7 denote the pH measurements, let 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 Ho be rejected?
b. Generate 10,000 samples X;.., X; from the true distribution of pH measurements.
For each sample, compute the test statistic and determine whether Ho is rejected.
Estimate the power of the test.
Transcribed Image Text: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 Ho : H = 7 versus H1 : µ z 7 will be made using the Student's t test (Section 6.4). Assume that the true mean is u = 6.5, the pH measurements are normally distributed with mean µi and standard deviation 0.5, and the test is made at the 5% level. a. Let X1, .., X7 denote the pH measurements, let 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 Ho be rejected? b. Generate 10,000 samples X;.., X; from the true distribution of pH measurements. For each sample, compute the test statistic and determine whether Ho is rejected. Estimate the power of the test.
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