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
d. \\( h_{0}: \mu \geq 33 \\)
\\( h_{a}: \mu<33 \\)
e. \\( h_{0}: \mu = 33 \\)
\\( h_{a}: \mu<33 \\)
f. \\( h_{0}: \mu>33 \\)
\\( h_{a}: \mu \leq 33 \\)
(b) use technology to find the p - value.
\\( p = 0.018 \\) (round to three decimal places as needed.)
(c) decide whether to reject or fail to reject the null hypothesis.
which of the following is correct?
a. fail to reject \\( h_{0} \\) because the p - value is greater than the significance level.
b. reject \\( h_{0} \\) because the p - value is less than the significance level.
c. fail to 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.

Explanation:

Step1: Compare P - value and significance level

Given \(P = 0.018\) and \(\alpha=0.05\).
Since \(0.018<0.05\) (i.e., \(P - value<\alpha\)).

Step2: Make decision based on rule

The rule is: If \(P - value<\alpha\), reject \(H_0\); if \(P - value\geq\alpha\), fail to reject \(H_0\).

Answer:

B. Reject \(H_0\) because the \(P\) - value is less than the significance level.