Question

According to a study, a cup of coffee contains an average of 112 milligrams (mg) of caffeine, with the amount per cup ranging from 60 to 186 mg. Suppose you want to repeat the experiment in order to obtain an estimate of the mean caffeine content in a cup of coffee correct to within 6 mg with 99% confidence. How many cups of coffee would have to be included in your sample?

The experiment must sample ____________ cups of coffee in order to estimate the mean caffeine content in a cup of coffee correct to within 6 mg with 99% confidence. (Round up to the nearest whole number.)

Answer 1

Solution :

Given that,

Population standard deviation = = (186 - 60) / 4 = 31.5

Margin of error = E = 6

Z_/2 = 2.576

sample size = n = [Z_/2* / E] ²

n = [2.576 * 31.5 / 6]²

n = 183

The experiment must sample 183 cups of coffee in order to estimate the mean caffeine content in a cup of coffee correct to within 6 mg with 99% confidence