Question

A market surveyor wishes to know how many energy drinks teenagers drink each week. They want to construct a 80%80% confidence interval with an error of no more than 0.070.07. A consultant has informed them that a previous study found the mean to be 3.63.6 energy drinks per week and found the variance to be 1.441.44. What is the minimum sample size required to create the specified confidence interval? Round your answer up to the next integer.

Answer 1

481

Explanation:

Given:

Variance = 1.44

S.d = √1.44 = 1.2

C.I = 80%

Margin of error, E = 0.07

Mean = 3.6

Using Z table, the Z score for 80% confidence interval, Zc = 1.28

To find the sample size, n, we have:

`n= [(Z_c * s.d)/(E)]^2`

Substituting figures in the formula, we have:

`n = [(1.28 * 1.2)/(0.07)]^2`

n = 21.94286²

n = 481.49

Approximately, n = 481