You receive a brochure from a large university. The brochure indicates that the mean class size for full-time faculty is fewer than 32students. 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 =0.10,can you support theuniversity's claim? Complete parts (a) through (d) below. Assume the population is normally distributed.

32 25 28 35 31 42 25 24 27 29 30 38 34 29 26 31 27 25

(a) Write the claim mathematically and identify Ho and Ha.

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

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

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