A random sample of 77 eighth grade? students' 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 the? state's eighth graders on this exam is more than 280. Assume that the population standard deviation is 40. At α=0.01?, is there enough evidence to support the? administrator's claim?

Find the standardized test statistic? z, and its corresponding area.

Find the? P-value.

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

At the 1% significance? level, there____ enough evidence to_______the? administrator's claim that the mean score for the? state's eighth graders on the exam is more than 280.