You wish to test the following claim ($\displaystyle {H}_{{a}}$) at a significance level of $\displaystyle \alpha={0.001}$.

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

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

Sample #1	Sample #2
63.4 41.7 36.1 52.6 43.2 54.5 69.8 69.8 46.5 52.6 74.9 53.7 48.6 62.7 50.7 51.8 49.2 43.7 59.8 55.3 44.6 50.1	57.1 45.9 67.1 68.5 67.9 62.1 56.1 58.6 62.9 57.1 54.3 63.6 60.9 58.8 65.1 69.9 52.3 66.8 57.5

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? For this calculation, use the degrees of freedom reported from the technology you are using. (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...