The FDA Is Comparing the Mean Caffeine Contents of Two

question 36

Multiple Choice

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

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 $95 \%$ reliability?

• A) \(n _ { 1 } = n _ { 2 } = 57\)
• B) \(n _ { 1 } = n _ { 2 } = 21\)
• C) \(n _ { 1 } = n _ { 2 } = 18\)
• D) \(n _ { 1 } = n _ { 2 } = 42\)

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