Quick note for SPSS users:  To get SPSS to run the analysis in the correct “direction” from the Analyze > Compare Means > Paired-Samples T Test... protocol, please enter the after variable first, and the before variable second.  (SPSS analyzes using first variable minus second variable.)

You wish to test the following claim ($\displaystyle {H}_{{a}}$) at a significance level of $\displaystyle \alpha={0.05}$. For the context of this problem, $\displaystyle \mu_{{d}}=\mu_{{2}}-\mu_{{1}}$ where the first data set represents a pre-test and the second data set represents a post-test.

      $\displaystyle {H}_{{o}}:\mu_{{d}}={0}$
      $\displaystyle {H}_{{a}}:\mu_{{d}}>{0}$

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
47.6	51.5
51.2	62.8
49.1	65.5
66	63.5
49.8	79.2
62.3	56.7
38.8	44.3
35.6	48.8
53.6	70
53.6	63.4
66	85.8
53.4	68.9
53.8	53.2
45	41.1
51.8	69.2
46.1	45.2
65.2	73.3
49.3	39.9
60.6	67.1
50.6	57.1
52.8	51.6

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...

This test statistic leads to a decision to...

As such, the final conclusion is that...