EXAMPLE 5 Confidence interval for

Use the “before” and “after” quiz scores from Table 1 to construct a 95% confidence interval for the population mean of the differences in the statistics quiz scores.

Solution

The normality of the quiz scores was checked in Example 2. We ignore the original raw data (see Table 1) and concentrate only on the set of sample differences: {16, 13, 14, 18, 14, 11, 12}. From Example 2, we have

For 95% confidence with degrees of freedom, equals 2.447 (see the table in Appendix Table D). Using these values,

We are 95% confident that the population mean of the differences between quiz scores before and after visiting the Math Center lies between 11.7983 points and 16.2017 points. If no mean change in the quiz scores occurred, the difference would be 0, which is not in this confidence interval. Thus, we have evidence that the Math Center tutoring leads to a significant change in the mean quiz scores, with 95% confidence.