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	457
4	574	606
5	448	414
6	502	526
7	480	430
8	499	459
9	610	615
10	572	541
11	390	329
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 =

(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

Answer 1

Student	Math	Writing	Difference(d)
1	540	474	66
2	432	380	52
3	528	457	71
4	574	606	-32
5	448	414	34
6	502	526	-24
7	480	430	50
8	499	459	40
9	610	615	-5
10	572	541	31
11	390	329	61
12	593	613	-20
		Total	324

a)

The null and alternative hypothesis is

H₀: μ_d = 0

H_a: μ_d ≠ 0

Level of significance = 0.05

Sample size = n = 12

Sample mean of difference = = 27

Sample standard deviation of difference = = 37.3144

Test statistic is

Degrees of freedom = n - 1 = 12 - 1 = 11

P-value = 2*P(T > 2.51) = 0.0292

b)

The point estimate of the difference between the mean scores for the two tests = Sample mean of difference = = 27

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

Math = = 514

Writing = = 487