Question

according to a food and drug administration (FDA) study, a cup of coffee contains an average of 115 mg of caffeine, with the amount per cup ranging from 60-180 mg. suppose u want to repeat the FDA experiment in order to obtain an estimate of the mean caffeine content in a cup of coffee correct to withing 5 mg with 95% confidence. how many cups of coffee would have be included in your sample?

Answer 1

Answer: 139

Explanation:

As per given , we have

The amount of caffeine per cup is ranging from 60-180 mg.

Range = Maximum - Minimum = 180 -60 =12

According to Range -rule ,

Standard deviation =
`s\approx(Range)/(4)=(120)/(4)=30`

Formula for sample size :
`n=((z^** s)/(E))^2` , where z* is critical z value and E is margin of error.

By z-table , the critical z-value for 95% confidence interval = 1.96

E= 5

Put all values in formula , we get

`n=(((1.96)* 30)/(5))^2=138.2976\approx139`

Hence, 139 cups of coffee would have be included in the sample.