Question

A standardized exam consists of three parts: math, writing, and critical reading. Sample data showing the math and writing scores for 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	414
6	502	526
7	480	430
8	499	453
9	610	615
10	572	541
11	390	335
12	593	613

(a)

Use a 0.05 level of significance and test for a difference between the population mean for the math scores and the population mean 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 three decimal places.)___

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

p-value = ____

What is your conclusion?

Reject H₀. We cannot conclude that there is a significant difference between the population mean scores for the math test and the writing test.

Do not reject H₀. We cannot conclude that there is a significant difference between the population mean scores for the math test and the writing test.     

Reject H₀. We can conclude that there is a significant difference between the population mean scores for the math test and the writing test

.Do not reject H₀. We can conclude that there is a significant difference between the population mean scores for the math test and the writing test.

(b)

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

What are the estimates of the population mean scores for the two tests?

Math_____

Writing____

Which test reports the higher mean score?

The math test reports a ( higher or lower) mean score than the writing test.

Answer 1

Answer:-

From the above information we perform two sample t test by using minitab for this we test the hypothesis

Where

is the difference between the population mean scores for the math test and the writing test.

Path :- stat - basis statistics - two sample t test

From the above output

The test statistic , T-value = 0.770

The P-value = 0.4470 at 0.05 level of significance

Decision :- P-value > level of significance , so accept Ho.

Conclusion:- Do not reject H0. We cannot conclude that there is a significant difference between the population mean scores for the math test and the writing test.

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