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. reject \\( h_{0} \\) because the p - value is less than the significance level.
b. reject \\( h_{0} \\) because the p - value is greater than the significance level.
c. fail to reject \\( h_{0} \\) because the p - value is less than the significance level.
d. fail 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.
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.
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.
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.
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:

When conducting a hypothesis test, if the P - value is greater than the significance level ($\alpha = 0.05$ in this case), we fail to reject the null hypothesis ($H_0$). The original claim is that the mean number of classroom hours per week for full - time faculty is $\mu=11.0$. Failing to reject $H_0$ means there is not enough evidence to reject the claim that the mean is 11.0.

Answer:

D. Fail to reject $H_0$ because the P - value is greater than the significance level.
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.