The FDA wants to compare the mean caffeine contents of two other brands of 6-oz. cola, Brand A and Brand B. Independent random samples of 6-oz. cans of each brand were selected and the caffeine content of each can be determined. The study provided the following summary information.

Construct a 99% confidence interval for the true difference between the mean caffeine contents of 6-oz. cans of Brand A and Brand B cola.

**Solution: **First of all we have to determine whether the variances can be considered equal or not. To that end, we use an F-test for variances. The outcome is shown in the table below:

This shows that we fail to reject the null hypothesis of equal variances (p = 0.6832). Given that we can assume that the variances are equal, the 99% confidence interval for the true difference between the mean caffeine contents of 6-oz. cans of Brand A and Brand B cola is given by

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