This problem is partially based on problem 12.1 from Lomax & Hahs-Vaughn, 3rd ed.

A 1-way fixed-effects ANOVA is performed on data for 4 groups of equal sizes ($\displaystyle {n}={12}$ subjects in each group), and $\displaystyle {H}_{{0}}$ is rejected at the $\displaystyle \alpha={0.05}$ level of significance.  The intent is to test the contrast: $\displaystyle \overline{{{Y}}}_{{\cdot{2}}}-\overline{{{Y}}}_{{\cdot{4}}}={0}$ (Thought for reflection:  What is actually being tested with this contrast?)

For this data, the error variance was estimated as $\displaystyle {M}{S}_{{\text{with}}}={52.7}$.  The sample means for each level of the factor were

Level	Mean
1	52.4
2	55.2
3	53.3
4	49.1

Follow these calculations to assess the contrast:
$\displaystyle \psi=$
      (report accurate to 1 decimal place)
$\displaystyle {s}_{\psi}=$
      (report accurate to 3 decimal place)
t-ratio:  $\displaystyle {t}=\frac{\psi}{{s}_{\psi}}=$
      (report accurate to 3 decimal place)
degrees of freedom for testing this contrast:  $\displaystyle {d}{f}=$
P-value:  $\displaystyle {p}=$
      (report accurate to 4 decimal place)