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A random sample of 89 eighth grade students' scores on a national mathematics assessment test has a mean score of 286. This test result prompts a state school administrator to declare that the mean score for the state's eighth graders on this exam is more than 280. Assume that the population standard deviation is 31. At a = 0.06, is there enough evidence to support the administrator's claim? Complete parts (a) through (e). (a) Write the claim mathematically and identify Ho and Ha. Choose the correct answer below. O A. Ho: us 280 (claim) OB. Ho: us 280 O C. Ho: H = 280 Ha: [ > 280 Ha: [ > 280 (claim) Ha: H > 280 (claim) O D. Ho: H 280 (b) Find the standardized test statistic z, and its corresponding area. z= (Round to two decimal places as needed.) (c) Find the P-value. P-value = (Round to three decimal places as needed.) (d) Decide whether to reject or fail to reject the null hypothesis. O Fail to reject Ho O Reject Ho (e) Interpret your decision in the context of the original claim. At the 6% significance level, there enough evidence to the administrator's claim that the mean score for the state's eighth graders on the exam is more than 280