A random sample of 88 eighth grade students score on a national mathematics assessment test has a mean score of 282. This test results prompts a state school administrator to declare that the mean score for the states eighth graders on this exam is more than 275. Assume that the population standard deviation is 30. At a=.03, is there enough evidence to support the administrator's claim? Complete parts b through d.

B. Find the standardized test statistic z, and it's corresponding area.

C. Find the P-value. Recall that a standard normal distribution table gives the area to the left of a z-score.

D. Decide whether to reject or fail to reject the null hypothesis.

E. Interpret your decision in the context of the original claim.