Question

A market research company wishes to know how many energy drinks adults drink each week. They want to construct a 98% confidence interval with an error of no more than 0.07. A consultant has informed them that a previous study found the mean to be 7.3 energy drinks per week and found the standard deviation to be 1.2. What is the minimum sample size required to create the specified confidence interval? Round your answer up to the next integer.

Answer 1

Sample size= 1590

Explanation:

Standard deviation = 1.2

Confidence interval = 98%

Margin of error to be no more than E = 0.07

Mean = 7.3

We determine the Z score from the Z table at 98% confidence interval = 2.326

Margin of error=Z score * Standard deviation/ root of sample size

0.07=2.326 * 1.2/root of sample size

Sample size n= (2.326 * 1.2/0.07)2

Sample size= 1590

Reference

Rumsey, D. J. (2007). Intermediate statistics for dummies. John Wiley & Sons.