This problem demonstrates a possible (though rare) situation that can occur with group comparisons.  The groups are sections and the dependent variable is an exam score.

Section 1	Section 2	Section 3
67	54.9	55.6
76.4	57.3	65.6
52.3	50	57.3
60.1	49.1	66.4
59	75.6	73
62.1	72	63.8
72.7	35.9	67
70.7	33.3	70.5
67.9	60.1	62.5

This data set can be downloaded in serial format with this link:  Download CSV

Run a one-factor ANOVA (fixed effect) with $\displaystyle \alpha={0.05}$.  Report the F-ratio to 3 decimal places and the P-value to 4 decimal places.
$\displaystyle {F}=$
$\displaystyle {p}=$
What is the conclusion from the ANOVA?

Calculate the group means for each section:
Section 1:  $\displaystyle {M}_{{1}}=$
Section 2:  $\displaystyle {M}_{{2}}=$
Section 3:  $\displaystyle {M}_{{3}}=$
Report means accurate to 2 decimal places.

Conduct 3 independent sample t-tests for each possible pair of sections.  (Though we will see later that it might not be appropriate, retain the significance level $\displaystyle \alpha={0.05}$.)  Report the P-value (accurate to 4 decimal places) for each pairwise comparison.
Compare sections 1 & 2:  $\displaystyle {p}=$
Compare sections 1 & 3:  $\displaystyle {p}=$
Compare sections 2 & 3:  $\displaystyle {p}=$
Based on these comparisons, which pair of groups have statistically significantly different means?

Thought for reflection:  What do the results of the pairwise comparisons suggest about the original conclusion from the ANOVA?