Question

A college administrator wanted to make all freshmen live on campus, because he thought that this would lead to better study habits and better grades. He commissioned a study that found a P‑value less than 0.05 for the difference in GPAs between freshmen who lived on campus and freshmen who commuted. The average GPA for the random sample of freshmen who lived on campus was 2.53, and the average GPA for the random sample of freshmen who commuted was 2.51. When he presented his findings, his idea was rejected.

What reason was he most likely given for this rejection?

a. The calculations from the study were likely incorrect.
b. The difference was not practically significant.
c. The difference was not statistically significant.

Answer 1

b. The difference was not practically significant.

Explanation:

Let mu1 be the mean GPA of freshmen who lived on campus

And mu2 be the mean GPA of freshmen who commuted

• 
  `H_(0)`: mu1-mu2=0

• 
  `H_(a)`: mu1-mu2>0

Since p-value of test statistic<0.05, the result is statistically significant

But the offer to make all freshmen live on campus is rejected likely due to it is being not practically significant.

Although the result is statistically significant, the effect size of the action (making all freshmen live on campus and moving their GPA's from 2.51 to 2.53) would not be worth to make the decision.

Thus the result is not practically significant.