Question

You wish to test the following claim (HaHa) at a significance level of α=0.001α=0.001. 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=0Ho:μd=0
      Ha:μd≠0Ha: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:

pre-test	post-test
53.7	159.8
47.5	33.5
46.9	9
54.6	102.5
55.6	77.2
48.5	117.2
49.7	30.7
56.1	-3
54	11.5
50.3	23.6
47.5	59.5
46.6	8.7
49	39.9
53.2	85.6
47.1	45.3
43.6	-42.9
55.4	41.4
58.8	102.4
47.2	-16.5

What is the test statistic for this sample?
test statistic =  (Report answer accurate to 4 decimal places.)

What is the p-value for this sample?  
p-value =  (Report answer accurate to 4 decimal places.)

Answer 1

Number	Post Test	Pre Test	Difference
	159.8	53.7	106.1	12167.2511
	33.5	47.5	-14	95.9368698
	9	46.9	-37.9	1135.33529
	102.5	54.6	47.9	2714.95845
	77.2	55.6	21.6	665.911607
	117.2	48.5	68.7	5315.1774
	30.7	49.7	-19	218.884238
	-3	56.1	-59.1	3013.43213
	11.5	54	-42.5	1466.48687
	23.6	50.3	-26.7	506.013186
	59.5	47.5	12	262.610554
	8.7	46.6	-37.9	1135.33529
	39.9	49	-9.1	23.9584488
	85.6	53.2	32.4	1339.94529
	45.3	47.1	-1.8	5.78529086
	-42.9	43.6	-86.5	6772.42371
	41.4	55.4	-14	95.9368698
	102.4	58.8	43.6	2285.34319
	-16.5	47.2	-63.7	3539.62371
Total	885.4	965.3	-79.9	42760.3495

Ho:μd=0
Ha:μd≠0

Test Statistic :-





t = -0.3761

Test Criteria :-
Reject null hypothesis if


Result :- Fail to reject null hypothesis

Decision based on P value
P - value = P ( t > 0.3761 ) = 0.7112
Reject null hypothesis if P value < level of significance
P - value = 0.7112 > 0.001 ,hence we fail to reject null hypothesis
Conclusion :- Fail to reject null hypothesis

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