The FDA Is Comparing the Mean Caffeine Contents of Two

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) $n _ { 1 } = n _ { 2 } = 42$