Questions on a statistics exam are considered good questions provided the questions discriminate between students who have studied for the exam and those who have not studied. Suppose that on a particular statistics exam the students were separated into two groups, the group that studied and the other group that had not studied. Data was collected and a 95% confidence interval for the difference in the proportion of those passing the exam from the group that studied and the proportion of those passing the exam from the group that had not studied. The confidence interval turned out to be (−0.005,0.125). Note that sample 1 is from the group that studied and sample 2 is from the group that did not study. Select the best answer.

A. We are 95% confident that there is no statistically significant difference between the passing rates of those who studied and those who did not study.
B. We are 95% confident that those who studied had a higher passing rate than those who did not study.
C. We are 95% confident that those who studied had a lower passing rate than those who did not study.
D. None of the these are correct.

The confidence interval for the difference in the proportion of those passing the exam from the group that studied and the proportion of those passing the exam from the group that had not studied is (-0.005, 0.125)

The lower bound of the difference in proportion is -0.005 while the upper bound is 0.125

Margin of error (E) = [0.125-(-0.05)] ÷ 2 = 0.13÷2 = 0.065

p1 - p2 (difference in proportion) = upper bound - E = 0.125 - 0.065 = 0.06

Since the difference in proportion is positive, we are 95% confident that those who studied had a higher passing rate than those who did not study.