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	374
3	528	463
4	574	612
5	448	420
6	502	520
7	480	430
8	499	459
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?

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.     

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 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  ---Select--- higher lower mean score than the writing test.

Answer 1

(a) Formulate the hypotheses.

H₀: μ_d = 0 H_a: μ_d ≠ 0

Calculate the test statistic.

2.448

p-value = 0.0324

What is your conclusion?

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.)

26

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

Math = 514

Writing = 488

Which test reports the higher mean score?

The math test reports a higher mean score than the writing test.

The output is:

514.000	mean Math
488.000	mean Writing
26.000	mean difference (Math - Writing)
36.799	std. dev.
10.623	std. error
12	n
11	df
2.448	t
.0324	p-value (two-tailed)