You receive a brochure from a large university. The brochure indicates that the mean class size for full-time faculty is fewer than 32 students. You want to test this claim. You randomly select 18 classes taught by full-time faculty and determine the class size of each:

35 28 29 33 32 40 26 25 29 28 30 36 33 29 27 30 28 25

a) Find the sample mean and sample standard deviation of the data.

b) At = 0.05, can you support the university's claim? (Show entire hypothesis test)