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) Should the water temperature be judged acceptable with a = 0.05?
(b) What is the P-value for this test?
(c) What is the probability of accepting the null hypothesis at a = 0.05 if the water has a true mean temperature of 104 °F?