You wish to test the following claim ($\displaystyle {H}_{{a}}$) at a significance level of $\displaystyle \alpha={0.002}$.

      $\displaystyle {H}_{{o}}:\mu_{{1}}=\mu_{{2}}$
      $\displaystyle {H}_{{a}}:\mu_{{1}}\ne\mu_{{2}}$

You believe both populations are normally distributed, but you do not know the standard deviations for either. Assume you should use a non-pooled test. You obtain the following two samples of data.

Sample #1	Sample #2
88.9 91.8 83.6 54.7 49.3 66 88.9 53.7 61.1 77.7 74.2 72.1	56.4 51.8 50.2 66.5 55.9 71.6 65.3 62.5 60.2 55.9 65.3 59.1 64.7 51.1 51.8 60.6 53.8 49.2 60.6 46 53.3

What is the critical value for this test? For this calculation, use the degrees of freedom reported from the technology you are using. (Report answer accurate to three decimal places.)
critical value = $\displaystyle \pm$

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...