Question

Most water-treatment facilities monitor the quality of their drinking water on an hourly basis. One variable monitored is pH, which measures the degree of alkalinity or acidity in the water. A pH below 7.0 is acidic, one above 7.0 is alkaline, and a pH of 7.0 is neutral. One water-treatment plant has a target pH of 8.5. 11 water samples are drawn at this plant. The plant wants to know if the median pH level in the water differs from 8.5.

0.22,13.35, 8.72, 8.93, 0.11, 8.23, 8.12, 13.15, 0.35, 0.75, 13.90

Write the null hypothesis and alternative hypothesis with the formula and full sentences.

what will we us the population mean or median

Using MINITAB for the p-value at α = 0.05 for the hypothesis test is it reject or fail to reject, and  is it Type I or Type II

Answer 1

The hypothesis being tested is:

H0: n = 8.5

H0: The median pH level in the water is 8.5

Ha: n ≠ 8.5

Ha: The median pH level in the water differs from 8.5

We will use the population median.

The Minitab output is:

Since the p-value (1) is greater than the significance level (0.05), we fail to reject the null hypothesis.

Therefore, we cannot conclude that the median pH level in the water differs from 8.5.

This is a Type II error.

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