Question

A market researcher wants to conduct a survey to estimate the population proportion who prefer Coca-Cola to Pepsi. Before conducting the survey, the researcher wants to choose a sample size so that the half width of the 99% confidence interval is no more than 2%, regardless what he will find. What is the required sample size?

Hints: recall that we only deal with "large n" population proportion questions in the class, so use the Z distribution. Also recall that the worst case for p-hat is when p-hat = 0.5.

Answer 1

Sample size = Z²/2 * ( 1 - ) / E²

= 2.5758² * 0.5 * 0.5 / 0.02²

= 4146.7

n = 4147 (Rounded up to nearest integer)