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You wish to test the following claim (H_a) at a significance level of alpha = 0.01. For the context of this problem, mu_d = mu_2 - mu_1 where the first data set represents a pre-test and the second data set represents a post-test. You believe the population of difference scores is normally distributed, but you do not know the standard deviation. You obtain pre-test and post-test samples for n = 47 subjects. The average difference (post - pre) is d = 1.3 with a standard deviation of the differences of s_d = 15.4. What is the test statistic for this sample? What is the p-value for this sample?

Solution

For a test statistic 0.5787

degree of freedom = n-1 = 47-1 = 46

We can use the calculator or t table or link http://www.socscistatistics.com/pvalues/tdistribution.aspx

to get p value for this test statistic

Enter 46 for df and one tail to get p value as 0.2828