A random sample of 77 eighth gradestudents' scores on a national mathematics assessment test has a mean score of 285. This test result prompts a state school administrator to declare that the mean score for thestate's eighth graders on this exam is more than 280. Assume that the population standard deviation is 40. At =0.01, is there enough evidence to support theadministrator's claim?

Find the standardized test statisticz, and its corresponding area.

Find theP-value.

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

At the 1% significancelevel, there____ enough evidence to_______theadministrator's claim that the mean score for thestate's eighth graders on the exam is more than 280.