Question: A test of abstract reasoning is given to a random sample of students before and after they completed a formal logic course. The results are given below. Construct a 95% confidence interval for the mean difference between the before and after scores. Is there evidence to suggest the logic course improves abstract reasoning? You may assume that the differences for the dependent samples are normally distributed.

Before 74 83 75 88 84 63 93 84 91 77

After 73 77 70 77 74 67 95 83 84 75

Note: define \[d=\] before – after, then \[\bar{d}=3.7\] and \[s=4.95\].