Question

The Food and Drug Administration monitors the production line of a breakfast cereal company to determine what proportion of its boxes of cereal contain insect parts. The FDA would like to know that proportion to within 5 percentage points with 95% confidence. How many boxes of cereal should they sample?

Answer 1

Answer: They should sample at-least 385 boxes of cereal .

Step-by-step explanation:

Let p be the proportion of boxes of cereal contain insect parts.

Given : The FDA would like to know that proportion to within 5 percentage points with 95% confidence.

i.e. margin of error : E= 0.05

We know that the z-value for 95% confidence = $z_c=1.96$

Since the prior proportion of boxes of cereal contain insect parts is unknown , so we assume p = 0.5

Formula to find the sample size :

$n=p(1-p)(\dfrac{z_{c}}{E})^2$

$\Rightarrow\ n=0.5(1-0.5)(\dfrac{1.96}{0.05})^2$

Simply , we get

$n=384.16\approx385$

Hence, they should sample at-least 385 boxes of cereal .