A random sample of 80 eighth grade students' scores on a national mathematics assessment test has a mean score of 273

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A random sample of 80 eighth grade students' scores on a national mathematics assessment test has a mean score of 273. 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 32. At a=0.03, is there enough evidence to support the administrator's claim? Complete parts (a) through (e). (a) Write the claim mathematically and identify Ho and Ha. Choose the correct answer below.
A. Ho: u = 270
Ha:p> 270 (claim)

B. Ho: u = 270 (claim)
Ha:p> 270

D. Ho: u270 (claim)

E. Ho: u<270> Ha: u > 270 (claim)

C. Ho:u  270
Ha:p> 270 (claim)

F. Ho: u> 270 (claim)
Ha:u<270> (b) Find the standardized test statistic z, and its corresponding area.
z =  __ (Round to two decimal places as needed.)
(c) Find the P-value.
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 3% significance level, there is not enough evidence to support the administrator's claim that the mean score for the state's eighth graders on the exam is