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 a = 0.10, can you reject the dean's ciaim? Complete parts (a) through (d) below. Assume the population is normally distributed. 10.9 7.8 12.4 8.1 7.7 10.4 14.7 9.20 (a) Write the claim mathematically and identify Ho and Hg. Which of the following correctly states Ho and H, ? DA Ho:<11.0 O B. Ho: us11.0 Ha: μ>11.0 O E. Ho >11.0 OC. Ho: H211.0 Hyi p211.0 Ha:H<11.0 D. Hg: p=11.0 OF. Ho: H#11.0 H: u =11.0 Hiu#11.0 Hgius11.0 (b) Use technology to find the P-value. P D (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? O A. Reject Ho because the P-value is less than the significance level. O B. Reject Ho because the P-value is greater than the significance level. O C. Fail to reject Ho because the P-value is greater than the significance level. D. Fail to reject Ho because the P-value is less than the significance level. (d) Interpret the decision in the context of the original claim. O A. At the 10% level of significance, there is not sufficient evidence to support O B. At the 10% level of significance, there is sufficient evidence to support the the claim that the mean class size for full-time faculty is more than 32 students. claim that the mean class size for full-time faculty is more than 32 students. O C. At the 10% level of significance, there is not sufficient evidence to support O D. At the 10% level of significance, there is sufficient evidence to support the the claim that the mean class size for full-time faculty is fewer than 32 students. claim that the mean class size for full-time faculty is fewer than 32 students