Helping smokers kick the habit is a big business in today's no-smoking environment. One of the more commonly used treatments according to an article in the Journal of Imagination, Cognition and Personality

(Vol. 12,1992193) is Spiegel's three-point message:

1. For your body, smoking is a poison.

2. You need your body to live.

3. You owe your body this respect and protection.

To determine the effectiveness of this treatment, the authors conducted a study consisting of a sample of 52 smokers placed in two groups, a Spiegel treatment group or a control group (no treatment). Each participant was asked to record the number of cigarettes he or she smoked each week. The results for the study are shown here for the beginning period and four follow-up time periods.

a. Create 95% confidence intervals for the difference in the average number of cigarettes smoked per week for the two groups for the beginning and each follow-up period. Interpret the results.

b. What assumptions are necessary for the validity of these confidence intervals?