Question

You may need to use the appropriate technology to answer this 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 CORRECT!!

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.)

Answer 1

Using Minitab<stats<basic Statistics<paired t test

Here is the output:

Paired T-Test and CI: Math, Writing

Descriptive Statistics

Sample	N	Mean	StDev	SE Mean
Math	12	514.0	68.3	19.7
Writing	12	488.0	93.9	27.1

Estimation for Paired Difference

Mean	StDev	SE Mean	95% CI for μ_difference
26.0	36.8	10.6	(2.6, 49.4)

µ_difference: mean of (Math - Writing)

Test

Null hypothesis	H₀: μ_difference = 0
Alternative hypothesis	H₁: μ_difference ≠ 0

T-Value	P-Value
2.448	0.032

Test Staistic=2.448

P value= 0.032

b) Point Estimate =math score − writing score.=514-488=26

Student	Math	Writing	d
1	540	474	66
2	432	374	58
3	528	463	65
4	574	612	-38
5	448	420	28
6	502	520	-18
7	480	430	50
8	499	459	40
9	610	615	-5
10	572	541	31
11	390	335	55
12	593	613	-20
		d-bar	26

Please do the comment for any doubt or clarification. Thank You!