Question: 387 women receiving free bone mineral density screenings were questioned. The questions focused on past smoking history. Sujbects undergoing hormone replacement therapy (HRT), and subjects not undergoing HRT, were asked if they had even been a regular smoker. In the HRT group 29.1 percent of 220 women stated that they were at some point in their life a regular smoker. In the non-HRT group, 17.9 percent of 106 women responded positively to being at some point in their life a regular smoker. (Sixty-one women chose not to answer the question).

Construct a 95% confidence interval for the difference in smoking percentages for the two populations of women represented by the subjects in this study and provide the assumptions necessary about the data, and verify that it is appropriate to use the confidence interval method based on the Central Limit Theorem for this problem.