A random sample of 83 eighth grade students\' scores on a national test has a me

Question

A random sample of 83 eighth grade students' scores on a national test has a mean score of 272. This test result prompts a state school administrator to declare that mean score for the state's eighth graders on this exam is more than 270. Assume that the population standard deviation is 34. At alpha = 0.09, is there enough evidence to support the administrator's claim? Complete parts (a) through (e). (a) Write the claim mathematically and identify H_0 and H_a. Choose the correct answer below. A. H_0: mu = 270 H_a: mu > 270 (claim) B. H_0: mu 270 F. H_0: 270 (claim) (b) Find the standardized test statistic t, and corresponding area. (Round to two decimal places as needed.) (c) Find the P-vale. P-value = (Round to three decimal places as needed.) (d) Decide whether to reject or fail to reject the null hypothesis. Reject H_0 fail to reject H_0 (e) your decision in the context of the original claim. At the 9% 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 270.

Explanation / Answer

Question a)

Answer: Option (D) Ho: µ 270

                                    Ha: µ > 270

Question b)

z = (x bar – Mean)/(sigma/sqrt(n))

     = (272 -270)/(34/sqrt(83))

     = 0.54

Answer: z = 0.54

Question c)

P-value:

Excel function = 1-normsdist(0.54) = 0.295

Answer: P-value = 0.295

Question d)

P-value > alpha

0.295 > 0.09

Answer: Fail to reject Ho

Question e)

At the 9% significance level there is not enough evidence to conclude to support the administrators claim .....

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