Question

# You wish to test the following claim ( H a ) at a significance level of...

You wish to test the following claim ( H a ) at a significance level of α = 0.02 . For the context of this problem, d = x 2 − x 1 where the first data set represents a pre-test and the second data set represents a post-test. 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:

pre-test post-test
27.1 5.1
32.8 69.7
60.2 64.4
59.2 127.2
53.5 59.6
41 43.3
36 70.2
44 45.3
59.2 136.4
51.9 90.2
36 51
48 48.3
45 36.3
40.7 27.8
62.8 51
35.7 -14.6
36.4 57.7
57.4 91.6
55.9 60.1
60.2 25.8
44.3 68.8

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 = The p-value is... less than (or equal to) α greater than α This test statistic leads to a decision to... reject the null accept the null fail to reject the null As such, the final conclusion is that... There is sufficient evidence to warrant rejection of the claim that the mean difference of post-test from pre-test is not equal to 0. There is not sufficient evidence to warrant rejection of the claim that the mean difference of post-test from pre-test is not equal to 0. The sample data support the claim that the mean difference of post-test from pre-test is not equal to 0. There is not sufficient sample evidence to support the claim that the mean difference of post-test from pre-test is not equal to 0.

The statistical software output for this problem is:

Hence,

Test statistic = 1.604

p - Value = 0.1243

greater than α

Fail to reject the null

Final conclusion: There is not sufficient sample evidence to support the claim that the mean difference of post-test from pre-test is not equal to 0.