Question

You wish to test the following claim (HaHa) at a significance level of α=0.05α=0.05. For the context of this problem, μd=μ2−μ1μd=μ2-μ1 where the first data set represents a pre-test and the second data set represents a post-test.

      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
52	69
51.6	34.7
48.3	55.4
31.6	46.8
46.4	42.6
31.6	27.1
49.3	49.3
33.1	57.3
22.3	44.4
56.6	43.6
62.5	63.7
66.4	118.1
62.5	64.3
31.6	49.2
41.8	81.2
52	53.8
65.7	106.5
55.4	94.8
67.3	66.7
45	43.8
35	30.5
27.6	37
56.6	33.4
39	63.9

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

Ho:μd=0
Ha:μd>0

Number	Post Test	Pre Test	Difference
	69	52	17	45.6187674
	34.7	51.6	-16.9	736.896267
	55.4	48.3	7.1	9.89626736
	46.8	31.6	15.2	24.5437674
	42.6	46.4	-3.8	197.285434
	27.1	31.6	-4.5	217.439601
	49.3	49.3	0	104.977101
	57.3	33.1	24.2	194.718767
	44.4	22.3	22.1	140.521267
	43.6	56.6	-13	540.368767
	63.7	62.5	1.2	81.8271007
	118.1	66.4	51.7	1718.44793
	64.3	62.5	1.8	71.3321007
	49.2	31.6	17.6	54.0837674
	81.2	41.8	39.4	849.965434
	53.8	52	1.8	71.3321007
	106.5	65.7	40.8	933.557101
	94.8	55.4	39.4	849.965434
	66.7	67.3	-0.6	117.632101
	43.8	45	-1.2	131.007101
	30.5	35	-4.5	217.439601
	37	27.6	9.4	0.71543403
	33.4	56.6	-23.2	1118.62377
	63.9	39	24.9	214.744601
Total	1377.1	1131.2	245.9	8642.93958

Test Statistic :-





t = 2.5893

Test Criteria :-
Reject null hypothesis if


Result :- Reject null hypothesis

Decision based on P value
P - value = P ( t > 2.5893 ) = 0.0082
Reject null hypothesis if P value < level of significance
P - value = 0.0082 < 0.05 ,hence we reject null hypothesis
Conclusion :- Reject null hypothesis