A politician claims that the mean salary for managers in his state is more than the national? mean, ?$83,000. Assume the the population is normally distributed and the population standard deviation is ?$9200. The salaries? (in dollars) for a random sample of 30 managers in the state are listed. At alpha (α) = 0.06?, is there enough evidence to support the? claim? Use technology.
70,489 83,282 77,567 73,183 98,660 71,211 80,448 83,068 74,215 79,541
99,729 83,139 91,927 92,992 99,415 80,659 93,658 74,725 78,794 81,207
86,462 75,416 89,736 99,769 76,254 84,131 87,481 95,401 89,341 90,806
?(a) Identify the null hypothesis and alternative hypothesis.
(b) Identify the standardized test statistic. (Round the final answer to two places as needed. Round all intermediate values to three places as needed)
(c) Find the P-value. Use technology (Round to three decimal places as needed)
(d) Decide whether to reject or fail to reject the null hypothesis