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A standardized exam consists of three parts: math, writing, andcritical reading. Sample data showing the math and writing scoresfor a sample of 12 students who took the exam follow.

Student	Math	Writing
1	540	474
2	432	380
3	528	463
4	574	612
5	448	420
6	502	526
7	480	430
8	499	459
9	610	609
10	572	541
11	390	329
12	593	613

(a)

Use a 0.05 level of significance and test for a differencebetween the population mean for the math scores and the populationmean for the writing scores. (Use math score − writing score.)

Formulate the hypotheses.

H₀:μ_d > 0

H_a:μ_d ≤ 0

H₀:μ_d ≤ 0

H_a:μ_d > 0

     

H₀:μ_d ≠ 0

H_a:μ_d = 0

H₀:μ_d = 0

H_a:μ_d ≠ 0

H₀:μ_d ≤ 0

H_a:μ_d = 0

Calculate the test statistic. (Round your answer to threedecimal places.)

Calculate the p-value. (Round your answer to fourdecimal places.)

p-value =

What is your conclusion?

Do not reject H₀. We cannot conclude thatthere is a significant difference between the population meanscores for the math test and the writing test. RejectH₀. We cannot conclude that there is asignificant difference between the population mean scores for themath test and the writingtest.      RejectH₀. We can conclude that there is a significantdifference between the population mean scores for the math test andthe writing test. Do not reject H₀. We canconclude that there is a significant difference between thepopulation mean scores for the math test and the writing test.

(b)

What is the point estimate of the difference between the meanscores for the two tests? (Use math score − writing score.)

What are the estimates of the population mean scores for the twotests?

Math Writing

Which test reports the higher mean score?

The math test reports a  ---Select--- higher lowermean score than the writing test.