Question

You wish to test the following claim ( H a ) at a significance level of α = 0.01 . 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: 51.5, 61.4, 54.2, 49.8, 47, 55.4, 50.3, 48, 47.6, 51.4, 44.2, 54.8, 56, 47.8, 53.3, 51.1

pre-test : 34.2, 28.5, 53.3, 78.9, 30.1, 28.8, 11.5, 17.4, 11.1, 25.3, 32.8, 43.4, 57.5 , 54.3,54.8 , 55.3

What is the test statistic for this sample?
What is the p-value for this sample? Round to 4 decimal places.

Answer 1

The table is as follows:

Pre-Test	Post-test	d (Difference = Post-test - Pre-test)
34.2	51.5	17.3
28.5	61.4	32.9
53.3	54.2	0.9
78.9	49.8	-29.1
30.1	47	16.9
28.8	55.4	26.6
11.5	50.3	38.8
17.4	48	30.6
11.1	47.6	36.5
25.3	51.4	26.1
32.8	44.2	11.4
43.4	54.8	11.4
57.5	56	-1.5
54.3	47.8	-6.5
54.8	53.3	-1.5
55.3	51.1	-4.2

d-bar = 12.91

sd = 18.86

The test statistic formula is:

t = (12.91 - 0)/(18.86/√16)

t = 12.91/4.715 = +2.74

The p-value associated with t = 2.74 and df = n - 1 = 15 is 0.0076.