Question

the dean of a university estimates that the mean number of classroom hours per week for full - time faculty is 11.0. as a member of the student council, you want to test this claim. a random sample of the number of classroom hours for eight full - time faculty for one week is shown in the table below. at \\( \alpha=0.05 \\), can you reject the deans claim? complete parts (a) through (d) below. assume the population is normally distributed.
10.4 9.4 13.1 7.2 7.7 9.2 13.1 8.6
(a) write the claim mathematically and identify \\( h_{0} \\) and \\( h_{a} \\).
which of the following correctly states \\( h_{0} \\) and \\( h_{a} \\)?
\\( \bigcirc \\) a. \\( h_{0}: \mu \leq 11.0 \\)
\\( h_{a}: \mu>11.0 \\)
\\( \bigcirc \\) b. \\( h_{0}: \mu<11.0 \\)
\\( h_{a}: \mu \geq 11.0 \\)
\\( \bigcirc \\) c. \\( h_{0}: \mu>11.0 \\)
\\( h_{a}: \mu \leq 11.0 \\)
\\( \bigcirc \\) d. \\( h_{0}: \mu = 11.0 \\)
\\( h_{a}: \mu \
eq 11.0 \\)
\\( \bigcirc \\) e. \\( h_{0}: \mu \geq 11.0 \\)
\\( h_{a}: \mu<11.0 \\)
\\( \bigcirc \\) f. \\( h_{0}: \mu \
eq 11.0 \\)
\\( h_{a}: \mu = 11.0 \\)

Explanation:

The dean's claim is that the mean number of classroom hours per week for full - time faculty is 11.0. In hypothesis testing, the null hypothesis \(H_0\) is the statement being tested (the claim in this case when it is a statement of equality), and the alternative hypothesis \(H_a\) is the statement that we are trying to find evidence for. Since the claim is about a specific value of the population mean (\(\mu = 11.0\)) and we are testing if we can reject this claim (a two - tailed test), the null hypothesis \(H_0:\mu = 11.0\) and the alternative hypothesis \(H_a:\mu
eq11.0\).

Answer:

D. \(H_0:\mu = 11.0\), \(H_a:\mu
eq11.0\)