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 (d) 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) what is the universitys claim?
\\( \bigcirc \\) a. fail to reject \\( h_0 \\) because the p - value is greater than the significance level.
\\( \bigcirc \\) b. reject \\( h_0 \\) because the p - value is less than the significance level.
\\( \bigcirc \\) c. fail to reject \\( h_0 \\) because the p - value is less than the significance level.
\\( \bigcirc \\) 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.
\\( \bigcirc \\) a. at the 5% level of significance, there is not sufficient evidence to support the claim that the mean class size for full - time faculty is more than 33 students.
\\( \bigcirc \\) b. at the 5% level of significance, there is not sufficient evidence to support the claim that the mean class size for full - time faculty is fewer than 33 students.
\\( \bigcirc \\) c. at the 5% level of significance, there is sufficient evidence to support the claim that the mean class size for full - time faculty is more than 33 students.
\\( \bigcirc \\) d. at the 5% level of significance, there is sufficient evidence to support the claim that the mean class size for full - time faculty is fewer than 33 students.

Explanation:

In hypothesis testing, if the P - value is less than the significance level ($\alpha$), we reject the null hypothesis ($H_0$). Here, the claim is that the mean class size for full - time faculty is fewer than 33 students. When we reject $H_0$ (because $P - value<\alpha = 0.05$), it means we have enough evidence to support the claim.

Answer:

D. At the 5% level of significance, there is sufficient evidence to support the claim that the mean class size for full - time faculty is fewer than 33 students.