QuestionYou 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 $\alpha=0.10$, can you support the university's claim? Complete parts (a) through (d) below. Assume the population is normally distributed.
37 31 30 31 35 33 41 24 22 29 뭄 29 33 28 27 (a) Write the claim mathematically and identify $\mathrm{H}_{0}$ and $\mathrm{H}_{\mathrm{a}}$.
Which of the following correctly states $\mathrm{H}_{0}$ and $\mathrm{H}_{\mathrm{a}}$ ? A. $\mathrm{H}_{0}: \mu>32$ B. $H_{0}: \mu \geq 32$ C. $\mathrm{H}_{0}: \mu=32$ $H_{a}: \mu \leq 32$ $H_{a}: \mu<32$ D. $H_{0}: \mu<32$ E. $H_{0}: \mu \leq 32$ $H_{a}: \mu \geq 32$ $H_{a}: \mu>32$ F. $\mathrm{H}_{0}: \mu=32$ $H_{a}: \mu \neq 32$ (b) Use technology to find the P -value. $P=$ $\square$ (Round to three decimal places as needed.)