SOLUTION: A university claim that their mean size class is no more than 32 students. To test this claim, one randomly selects 18 classes and determines the size of each. The results are here

Question 1009917: A university claim that their mean size class is no more than 32 students. To test this claim, one randomly selects 18 classes and determines the size of each. The results are here 35, 28, 29, 33, 32, 40, 26, 25, 29, 28, 30, 36, 33, 29, 27, 30, 28, 25. At a = 0.01, can one support the university's claim?
Found 2 solutions by rfer, Boreal:
Answer by rfer(16322) (Show Source): You can put this solution on YOUR website!
yes, but you do the math
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
mean is 27.05556
sx=9.17
n=18
Right off, the sample mean is less than the postulated mean, so there is insufficient evidence to show that the mean size class is more than 32 students. This is with a one-tail test. One-sided confidence intervals are tricky, but the two-sided is (20.788,33.323), as expected. For this to have any chance of significance, the mean of the sample has to be greater than 32.

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