Question

You wish to test the following claim (HaHa) at a significance level of α=0.005α=0.005. 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
48.6	37.2
53	73.8
69.1	78.9
43.7	35.4
51.7	50.9
48.3	38.7
54.7	58.1
39.5	47.1
62.7	72.1
53.2	44.5
58.6	64
62.7	66.5
56	60.9
67.3	64
51.4	45.9
44.2	34.6
53.2	48.3
62.7	63.6
40.2	40.9
48.9	57.7
51.1	33.3
45.5	35.3
40.9	44.1
60.8	56.2
58.1	59.8

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

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

Answer 1

pre-test	post-test	d = Post-test - Pre-test
48.6	37.2	-11.4
53	73.8	20.8
69.1	78.9	9.8
43.7	35.4	-8.3
51.7	50.9	-0.8
48.3	38.7	-9.6
54.7	58.1	3.4
39.5	47.1	7.6
62.7	72.1	9.4
53.2	44.5	-8.7
58.6	64	5.4
62.7	66.5	3.8
56	60.9	4.9
67.3	64	-3.3
51.4	45.9	-5.5
44.2	34.6	-9.6
53.2	48.3	-4.9
62.7	63.6	0.9
40.2	40.9	0.7
48.9	57.7	8.8
51.1	33.3	-17.8
45.5	35.3	-10.2
40.9	44.1	3.2
60.8	56.2	-4.6
58.1	59.8	1.7
	μd =	-0.572
	s =	8.670713158

(a)

Data:     

n = n1 = n2 = 25    

μd = -0.572    

s = 8.670713158    

Hypotheses:     

Ho: μd ≤ 0    

Ha: μd > 0    

Decision Rule:     

α = 0.05    

Degrees of freedom = 25 - 1 = 24

Critical t- score = 1.710882067   

Reject Ho if t > 1.710882067    

Test Statistic:     

SE = s/√n = 8.67071315790499/√25 = 1.734142632   

t = μd/SE = -0.572000000000001/1.734142631581 = -0.330

(b)

p- value = 0.3722    

Decision (in terms of the hypotheses):    

Since -0.329845994 < 1.711 we fail to reject Ho

Conclusion (in terms of the problem):    

There is no sufficient evidence that μd > 0    

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