Question

You wish to test the following claim (HaHa) at a significance level of α=0.01α=0.01. For the context of this problem, μd=PostTest−PreTestμd=PostTest-PreTest where the first data set represents a pre-test and the second data set represents a post-test. (Each row represents the pre and post test scores for an individual. Be careful when you enter your data and specify what your μ1μ1 and μ2μ2 are so that the differences are computed correctly.)
Ho:μd=0
Ha:μd≠0
You believe the population of difference scores is normally distributed, but you do not know the standard deviation. You obtain the following sample of data:

What is the test statistic for this sample?
test statistic =

What is the p-value for this sample?
p-value =

pre-test	post-test
40.6	57
46.2	22.8
35.2	7.9
42.2	27.6
37.7	91.2
40.3	54.7
31.1	48.2
30.1	73.8
30.1	65.2
41.8	26.4
43.9	36.7
43.5	97
49.9	25.3
44	59.1
39.7	56.1
35.8	29.3
45.5	40.9
37.4	53.8
38.9	33
42.3	51.7
41.4	24.2
30.7	53.7

Answer 1

Number	Post test	Pre test	Difference
	57	40.6	16.4	77.3600
	22.8	46.2	-23.4	961.2818
	7.9	35.2	-27.3	1218.3273
	27.6	42.2	-14.6	493.0418
	91.2	37.7	53.5	2106.3927
	54.7	40.3	14.4	46.1782
	48.2	31.1	17.1	90.1637
	73.8	30.1	43.7	1302.8818
	65.2	30.1	35.1	756.0000
	26.4	41.8	-15.4	529.2091
	36.7	43.9	-7.2	219.1746
	97	43.5	53.5	2106.3927
	25.3	49.9	-24.6	1037.1327
	59.1	44	15.1	56.1818
	56.1	39.7	16.4	77.3600
	29.3	35.8	-6.5	198.9382
	40.9	45.5	-4.6	148.9509
	53.8	37.4	16.4	77.3600
	33	38.9	-5.9	182.3727
	51.7	42.3	9.4	3.2237
	24.2	41.4	-17.2	615.2655
	53.7	30.7	23	237.0200
Total	1035.6	868.3	167.3	12540.2095

Test Statistic :-


t = 1.4596

Test Criteria :-
Reject null hypothesis if
Critical value t(/2) =   = 2.8314 ( From t table )

Result :- Fail to reject null hypothesis

Decision based on P value
P - value = P ( t > 1.4596 ) = 0.1592
Reject null hypothesis if P value < level of significance
P - value = 0.1592 > 0.01, hence we fail to reject null hypothesis
Conclusion :- Fail to reject null hypothesis

There is insufficient evidence to support the claim that Ha:μd≠0.

Test statistic = t = 1.4596

P value = P ( t > 1.4596 ) = 0.1592