The FDA Is Comparing the Mean Caffeine Contents of Two

question 9

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

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