A random sample of 87 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 40. At =0.04, is there enough evidence to support the administration's claim? Complete parts (a) through (e).

a) Write the claim mathematically and identify H0 and Ha. Choose the correct answer below.

b) Find the standardized test statistic z and its corresponding area. z= (round 2 decimal)

c) Find the P-value. P-value (round 2 decimal)

d) Decide whether to reject or fail to reject the null hypothesis. Reject H0 or Fail to reject