The FDA Is Comparing the Mean Caffeine Contents of Two

question 42

Short Answer

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) $n _ { 1 } = n _ { 2 } = 42$
B) $n _ { 1 } = n _ { 2 } = 18$
C) $n _ { 1 } = n _ { 2 } = 57$
D) $n _ { 1 } = n _ { 2 } = 21$

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

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Definitions:

Reorder Point

The inventory level at which a new order should be placed to replenish stock before it runs out, taking into account lead times.

Lead Time

The total time taken from the initiation of a process or order until its completion or delivery.

Fixed-Period Inventory System

An inventory control system where orders are made at fixed intervals, but the order quantity varies based on demand.

Safety Stock

Additional inventory held to guard against stockouts, ensuring that a sufficient quantity of goods is available to meet demand fluctuations.