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A random sample of 86 eighth grade​ students' scores on a national mathematics assessment test has...

A random sample of 86 eighth grade​ students' scores on a national mathematics assessment test has a mean score of 275. 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 270. Assume that the population standard deviation is 33. At alpha=0.05​, is there enough evidence to support the​ administrator's claim? Complete parts​ (a) through​ (e).

(a) Write the claim mathematically and identify H0 and Ha.

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

(c) Find the​ P-value.

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

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

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