A private opinion poll is conducted for a politician to determine what proportion of the population favors decriminalizing marijuana possession. How large a sample is needed in order to be 95% confident that the
Sample proportion will not differ from the true proportion by more than 4%?

Question

Quizplus · Accepted Answer

To achieve a 95% confidence level with a margin of error of 4% (0.04) when the population proportion is unknown, the formula for the sample size (n) is used: n = (Z^2 * p * (1-p)) / E^2. Assuming p = 0.5 (which maximizes the sample size) and Z = 1.96 for 95% confidence, the calculation is n = (1.96^2 * 0.5 * 0.5) / 0.04^2, which results in approximately 600.25, rounded up to the nearest whole number gives 601.

A Private Opinion Poll Is Conducted for a Politician to Determine