The mean water temperature downstream from a power plant cooling tower discharge pipe should be no more than 100°F. Past experience has indicated that the standard deviation of temperature is 2°F. The water temperature is measured on nine randomly chosen days, and the average temperature is found to be 98°F.

(a) Is there evidence that the water temperature is acceptable at  0.05?

(b) What is the P-value for this test?

(c) What is the probability of accepting the null hypothesis at  0.05 if the water has a true mean temperature of 104°F?