Question

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 $\alpha = 0.01$, can you support the universitys claim? complete parts (a) through (d) below. assume the population is normally distributed.
38 27 32 32 35 39 26 23 32
28 29 33 30 26 25 31 28 27
significance level.
○ b. fail to reject $h_0$ because the p - value is less than the significance level.
○ c. reject $h_0$ because the p - value is less than the significance level.
○ d. reject $h_0$ because the p - value is greater than the significance level.
(d) interpret the decision in the context of the original claim.
○ a. at the 1% level of significance, there is sufficient evidence to support the claim that the mean class size for full - time faculty is more than 32 students.
○ b. at the 1% level of significance, there is not sufficient evidence to support the claim that the mean class size for full - time faculty is fewer than 32 students.
○ c. at the 1% level of significance, there is sufficient evidence to support the claim that the mean class size for full - time faculty is fewer than 32 students.
○ d. at the 1% level of significance, there is not sufficient evidence to support the claim that the mean class size for full - time faculty is more than 32 students.

Explanation:

Step1: Hypothesis Testing Basics

In hypothesis testing, if the P - value is less than the significance level ($\alpha$), we reject the null hypothesis ($H_0$). Here, $\alpha = 0.01$.

Step2: Analyzing the Claim

The university's claim is that the mean class size for full - time faculty is fewer than 32 students. So, the null hypothesis $H_0:\mu\geq32$ and the alternative hypothesis $H_1:\mu < 32$.
If we reject $H_0$ (because $P - value<\alpha$), it means we support the claim (since $H_1$ is in line with the university's claim). If we fail to reject $H_0$ (because $P - value\geq\alpha$), we do not support the claim.

Answer:

C. Reject \(H_0\) because the P - value is less than the significance level.
B. At the 1% level of significance, there is not sufficient evidence to support the claim that the mean class size for full - time faculty is fewer than 32 students.