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
\\( \bigcirc \\) a. reject \\( h_{0} \\) because the p - value is less than the significance level.
\\( \bigcirc \\) b. reject \\( h_{0} \\) because the p - value is greater than the significance level.
\\( \bigcirc \\) c. fall to reject \\( h_{0} \\) because the p - value is less than the significance level.
\\( \vee \\) d. fall to 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 sufficient evidence to reject the claim that the mean number of classroom hours per week for full - time faculty is 11.0.
\\( \bigcirc \\) b. at the 5% level of significance, there is sufficient evidence to reject the claim that the mean number of classroom hours per week for full - time faculty is greater than 11.0.
\\( \bigcirc \\) c. at the 5% level of significance, there is not sufficient evidence to reject the claim that the mean number of classroom hours per week for full - time faculty is less than 11.0.
\\( \bigcirc \\) d. at the 5% level of significance, there is not sufficient evidence to reject the claim that the mean number of classroom hours per week for full - time faculty is 11.0.

Explanation:

In hypothesis testing, if the P - value is greater than the significance level ($\alpha$), we fail to reject the null hypothesis ($H_0$). Here, the claim is that the mean number of classroom hours per week for full - time faculty is 11.0 (which is the null hypothesis). Since we failed to reject $H_0$ (because P - value > $\alpha = 0.05$), it means there is not enough evidence to reject the claim.

Answer:

C. At the 5% level of significance, there is not sufficient evidence to reject the claim that the mean number of classroom hours per week for full - time faculty is 11.0.