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A random sample of 80 eighth grade​ students’ scores on a national mathematics assessment test has a mean score of 283. 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 38. At alpha equals 0.05​, is there enough evidence to support the​ administrator’s claim? Complete parts​ (a) through​ (e).