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A random sample of 76 eighth grade students' scores on a national mathematics assessment test has a mean score of 288. 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 285. Assume that the population standard deviation is 39. At or = 0.12, is there enough evidence to support the administrators claim? Complete parts (a) through (e). (a) Write the claim mathematically and identify H0 and Ha. Choose the correct answer below. iv:- A. Ho: p2285 (claim) {a B. H0: p5285 Ch 0. H0: p=285 (claim) Ha: p285 (claim) Ha: p>285 CI- D. HO: p=285 2] E. H0: p285 (claim) Ha: (12285 (claim) Ha: p>285 (b) Find the standardized test statistic z, and its corresponding area. 2: (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. Fail to reject Ho CI- Reject Ho (e) Interpret your decision in the context of the original claim. At the 12% signicance level, there V enough evidence to V the administrator's claim that the mean score for the state's eighth graders on the exam is more than 285