Hi Lin,

Is this really the way the problem was worded? Can you conclude that the group performed better on the second test? Of course they did. Four of the five students improved their grades and the average improvement was 3.8 points. You don’t need any statistics to see this, you just have to do the arithmetic. The problem should be worded something like this.

A teacher wanted to see if studying together improves the grades on statistics midterms. To do this she randomly selected 5 students who studied alone and recorded their grades on the first midterm. She then had them study together for the second midterm and recorded their grades. From the results is their sufficient evidence (at $\alpha = 0.0.$) to conclude that studying together improves performance?

Let $X$ be the random variable that is the score on the first midterm, $Y$ be the random variable that is the score on the second midterm and $d = Y – X.$ Let $\mu_X$ be the mean score on the first midterm for students who studied alone, $\mu_Y$ be the mean score on the second midterm for students who studied together and $\mu_d = \mu_Y - \mu_{X}.$ Use the data below to test the hypothesis that $\mu_d = 0$ against the alternate hypothesis that $\mu_d > 0.$

This is now a one sample t-test rather than a two sample test.

Can you complete the problem now? Write back if you need more assistance,
Penny