A politician claims that the mean salary for managers in his state is more than the national mean, $81,000. Assume the the population is normally distributed and the population standard deviation is $9100. The salaries (in dollars) for a random sample of 30 managers in the state are listed. At a = 0.05, is there enough evidence to support the claim? Use technology. 70,808 71,415 97,854 72,384 97,127 99,628 84,701 75,071 76,062 91,710 77,350 96,792 96,071 78,896 89,135 79,661 91,057 82,479 79,329 84,453 70,576 94,523 80,348 77,257 76,151 79,903 85,206 86,037 72,029 80,911 (a) Identify the null hypothesis and alternative hypothesis. OC. Ho: H#81,000 O A. Ho: H>81,000 Ha: us81,000 о в. Но: иs 81,000 Hại H>81,000 Ha:u=81,000 O D. Ho: H281,000 H:u<81,000 O E. Ho: = 81,000 HH481,000 OF. Ho: H>81,000 H:us81,000 (b) Find the P-value. Use technology. | (Round to three decimal places as needed.) (c) Decide whether to reject or fail to reject the null hypothesis. O A. Reject Ho. There is not sufficient evidence to support the claim that managers mean salary is O B. Fail to reject Ho. There is not sufficient evidence to support the claim that managers mean more than the national mean. salary is more than the national mean. OC. Reject Ho. There is sufficient evidence to support the claim that managers mean salary is more D. Fail to reject H,. There is sufficient evidence to support the claim that managers mean salary is more than the national mean. than the national mean.