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	414
6	502	526
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?

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. 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.

(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

SAMPLE 1	SAMPLE 2	difference , Di =sample1-sample2	(Di - Dbar)²
540	474	66.000	1600.000
432	374	58.000	1024.000
528	463	65.000	1521.000
574	612	-38.000	4096.000
448	414	34.000	64.000
502	526	-24.000	2500.000
480	430	50.000	576.000
499	459	40.000	196.000
610	615	-5.000	961.000
572	541	31.000	25.000
390	335	55.000	841.000
593	613	-20.000	2116.000

	sample 1	sample 2	Di	(Di - Dbar)²
sum =	6168	5856.00	312.000	15520.000

a)

Ho :   µd=   0
Ha :   µd ╪   0
      

mean of difference ,    D̅ =ΣDi / n =   26.000                  
                          
std dev of difference , Sd =    √ [ (Di-Dbar)²/(n-1) =    37.5621                  
                          
std error , SE = Sd / √n =    37.5621   / √   12   =   10.8432      
                          
t-statistic = (D̅ - µd)/SE = (   26   -   0   ) /    10.8432   =   2.398

Degree of freedom, DF=   n - 1 =    11  
  
p-value =        0.0354   [excel function: =t.dist.2t(t-stat,df) ]

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)

point estimate of the difference between the mean scores for the two tests=26.00

math=514

writing = 488

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