The National Weather Service says that the mean daily high temperature for Octob

Question

The National Weather Service says that the mean daily high temperature for October in a large Midwestern city is 56 degree F. A local weather service suspects that this value is not accurate and wants to perform a hypothesis test to determine whether the mean is actually lower than 56 degree F. A sample of mean daily high temperatures for October over the past 37 years yields x bar = 54 degree F. Assume that the population standard deviation is 5.6 degree F. Perform the hypothesis test at the 1% significance level.

Explanation / Answer

Mean = 56
Sample mean =54
n = 37
pop. devi = 5.6

Ho: Mu<56
Ha: Mu >= 56

Z = (54-56)/(5.6/sqrt(37)) = -2.17, which is not in critical region
The critical region by 1% is -2.325

Hence, we don't reject null hypothsisand say thay MU<56

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