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 liters when constructing a 99% confidence interval?
A)29
B)832
C)832.39
D)833

Question

Quizplus · Accepted Answer

To find the sample size, use the formula for the margin of error in a confidence interval: $ E = Z \times \frac{\sigma}{\sqrt{n}} $. For a 99% confidence interval, the Z-value is approximately 2.576. Rearrange the formula to solve for $ n $: $ n = \left(\frac{Z \times \sigma}{E}\right)^2 $. Plugging in the values: $ n = \left(\frac{2.576 \times 1.12}{0.1}\right)^2 \approx 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