A random sample of 84 eighth grade students' scores on a national mathematics assessment test has a mean score of 287. This test results 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 37. At a=0.02, is there enough evidence to support the administrator's claim?

(a) Write the claim mathematically and identify Ho and Ha

(b) Find the standardized test statistic z, and its corresponding area

(c) Find the P-value

(d) Decide whether to reject or fail to reject the null hypothesis