Question

You wish to test the following claim ( H a ) at a significance level of α = 0.005 . d denotes the mean of the difference between pre-test and post-test scores. H o : μ d = 0 H a : μ d ≠ 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: post-test pre-test 47.5 19.8 39.7 27.1 41.6 44 35.9 36.2 57.9 50.4 51.4 63.7 43.3 29.3 61.8 38.7 48.5 52.9 52.8 55.2 42 36.1 36.5 25.6 39.7 8.4 69.8 45.4 66.8 54.2 43.7 12.4 52.4 41.9 42.8 36.9 56.4 60.3 38.7 16.2 55.3 62.6 24.7 19.5

What is the test statistic for this sample? test statistic = Round to 3 decimal places. What is the p-value for this sample? Round to 4 decimal places. p-value = The p-value is... less than (or equal to) α greater than α

Answer 1

We have the following data:

Post-test	Pre-test	Difference (d)
47.5	19.8	27.7
39.7	27.1	12.6
41.6	44	-2.4
35.9	36.2	-0.3
57.9	50.4	7.5
51.4	63.7	-12.3
43.3	29.3	14
61.8	38.7	23.1
48.5	52.9	-4.4
52.8	55.2	-2.4
42	36.1	5.9
36.5	25.6	10.9
39.7	8.4	31.3
69.8	45.4	24.4
66.8	54.2	12.6
43.7	12.4	31.3
52.4	41.9	10.5
42.8	36.9	5.9
56.4	60.3	-3.9
38.7	16.2	22.5
55.3	62.6	-7.3
24.7	19.5	5.2

x_d (Mean) = 9.655
s_d = 12.831

Ho : μd = 0

Ha : μd ≠ 0

Let's calculate the test-statistic:

t = (x_d- μ_d)/(s_d/√n) = (9.655 - 0)/(12.831/√22)

t = 9.65/2.735 = 3.529

The p-value (two-tailed) at df = n - 1 = 21 is 0.0020

The p-value is less than α, so we reject the null hypothesis that there is no difference between the post-test and pre-test scores.