A marketing firm wants to estimate how much root beer the average teenager drinks per year. A previous study found a standard deviation of 1.12 liters. How many teenagers must the firm interview in order to have a margin of error of at most 0.1 liter when constructing a 99% confidence interval?
A) 831.39
B) 832
C) 832.39
D) 833

Question

Quizplus · Accepted Answer

To find the sample size, use the formula for margin of error in a confidence interval: ME = Z * (σ/√n). For a 99% confidence interval, Z is approximately 2.576. Solving for n gives n = (Z * σ / ME)^2 = (2.576 * 1.12 / 0.1)^2 ≈ 832.39. Since the sample size must be a whole number, round up to 833.

A Marketing Firm Wants to Estimate How Much Root Beer