A random sample of 82 eighth gradestudents' scores on a national mathematics assessment test has a mean score of 279. 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 270. Assume that the population standard deviation is 39. At =0.09, is there enough evidence to support theadministrator's claim? Complete parts(a) through(e).

(a) Write the claim mathematically and identify H0 and Ha. Choose the correct answer below.

A. H0: 270 (claim)

Ha: <270

B. H0: <270

Ha: 270 (claim)

C. H0: =270

Ha: >270 (claim)

D. H0: =270 (claim)

Ha: >270

E. H0: 270 (claim)

Ha: >270

F. H0: 270

Ha: >270 (claim)

(b) Find the standardized test statisticz, and its corresponding area.

z=________

(Round to two decimal places asneeded.)

(c) Find theP-value.

P-value=_________

(Round to three decimal places asneeded.)

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

Failtoreject H0

Reject H0

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

At the 9% significancelevel, there _______( is OR is not) enough evidence to __________ (support OR reject) theadministrator's claim that the mean score for thestate's eighth graders on the exam is more than 270.