You wish to test the following claim ($\displaystyle {H}_{{a}}$) at a significance level of $\displaystyle \alpha={0.01}$. 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
49.7	62.8
47.9	63.9
46.6	49.8
48.5	69.3

What is the critical value for this test? (Report answer accurate to three decimal places.)
critical value =

What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic =

The test statistic is...

This test statistic leads to a decision to...

As such, the final conclusion is that...