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The FDA Is Comparing the Mean Caffeine Contents of Two

question 9

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The FDA is comparing the mean caffeine contents of two brands of cola. Independent random samples of 6-oz. cans of each brand were selected and the caffeine content of each can determined. the study provided the following summary information.

 Brand A  Brand B  Sample size 1510 Mean 1820 Variance 1.21.5\begin{array}{lrr}\hline & \text { Brand A } & \text { Brand B } \\\hline \text { Sample size } & 15 & 10 \\\text { Mean } & 18 & 20 \\\text { Variance } & 1.2 & 1.5 \\\hline\end{array}

How many cans of each soda would need to be sampled in order to estimate the difference in the mean caffeine content to within . 5 with 95%95 \% reliability?

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