A random sample of 76 eighth grade​ students' scores on a national mathematics assessment test has a mean score of 294. This test result prompts a state school administrator to declare that the mean...

A random sample of

eighth grade​ students' scores on a national mathematics assessment test has a mean score of

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

Assume that the population standard deviation is

At

is there enough evidence to support the​ administrator's claim? Complete parts​ (a) through​ (e).

​(a) Write the claim mathematically and identify

and

Choose the correct answer below.

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

​(Round to two decimal places as​ needed.)

​(c) Find the​ P-value.

​(Round to three decimal places as​ needed.)

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

​(e) Interpret your decision in the context of the original claim.

At the

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