Question

you receive a brochure from a large university. the brochure indicates that the mean class size for full - time faculty is fewer than 33 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=0.05 \\), can you support the universitys claim? complete parts (a) through (c) below. assume the population is normally distributed.
37 30 26 33 35 42 24 22 28
29 27 39 30 32 24 27 29 28
(a) write the claim mathematically and identify \\( h_{0} \\) and \\( h_{a} \\).
which of the following correctly states \\( h_{0} \\) and \\( h_{a} \\)?
\\( \bigcirc \mathrm{a} \\). \\( h_{0}: \mu<33 \\)
\\( h_{a}: \mu \geq 33 \\)
\\( \bigcirc \mathrm{b} \\). \\( h_{0}: \mu=33 \\)
\\( h_{a}: \mu \
eq 33 \\)
\\( \bigcirc \mathrm{c} \\). \\( h_{0}: \mu \leq 33 \\)
\\( h_{a}: \mu>33 \\)
\\( \bigcirc \mathrm{d} \\). \\( h_{0}: \mu \geq 33 \\)
\\( h_{a}: \mu<33 \\)
\\( \bigcirc \mathrm{e} \\). \\( h_{0}: \mu=33 \\)
\\( h_{a}: \mu<33 \\)
\\( \bigcirc \mathrm{f} \\). \\( h_{0}: \mu>33 \\)
\\( h_{a}: \mu \leq 33 \\)

Explanation:

Step1: Understand the claim

The university claims that the mean class size for full - time faculty is fewer than 33 students. In hypothesis testing, the null hypothesis \(H_0\) is a statement of equality or no difference, and the alternative hypothesis \(H_a\) is the claim we are trying to find evidence for.

Step2: Set up the hypotheses

If the claim is \(\mu<33\), then the null hypothesis \(H_0\) (the opposite of the claim for the purpose of testing) is \(\mu\geq33\) and the alternative hypothesis \(H_a\) is \(\mu < 33\).

Answer:

D. \(H_0:\mu\geq33\), \(H_a:\mu < 33\)