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. The results are shown in the table below. At alpha equals 0.01, can you support the university's claim? Complete parts (a) through (d) below. Assume the population is normally distributed.

35 29 31 32 29 43 25 28 29

31 30 39 31 31 24 32 27 22

(a) Write the claim mathematically and identify Upper H 0 and Upper H Subscript a.

DO NOT ANSWER THIS QUESTION SKIP TO B

(b) Use technology to find the P-value.

P equals ____

(Round to three decimal places as needed.)

(c) Decide whether to reject or fail to reject the null hypothesis.

(d) Interpret the decision in the context of the original claim.