The mean water temperature downstream from a power plant cooling tower discharge

Question

The mean water temperature downstream from a power plant cooling tower discharge pipe should be no more than 101oF. Past experience has indicated that the standard deviation of temperature is 2oF. The water temperature is measured on 4 randomly chosen days, and the average temperature is found to be 98oF.

The mean water temperature downstream from a power plant cooling tower discharge pipe should be no more than 101 degree F. Past experience has indicated that the standard deviation of temperature is 2 degree F. The water temperature is measured on 4 randomly chosen days, and the average temperature is found to be 98 degree F. What is the probability of accepting the null hypothesis at alpha =0.05 if the water has a true mean temperature of 107 degree F? Round your final answer to four decimal places (e.g. 98.7654).

Explanation / Answer

X-101)/(2/sqrt(4)) = 2.35

--> X = 101 +2.35*(2/sqrt(4)) =103.35

So the probability is

P(xbar>103.35) = P(t with df=3>(103.35-107)/(2/sqrt(4)))

=P(t with df=3 >-3.65) =0.9823 (from student t table)

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