What sample size is needed to give a margin of error within $\pm 1.5 %$ in estimating a population proportion with $95 %$ confidence?

Round your answer up to the nearest integer.

Sample size $=$
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Answer

The sample size needed to give a margin of error within $\pm 1.5 %$ in estimating a population proportion with 95% confidence is $4269$ .

Steps

Step 1 ：Define the constants: the Z-score for a 95% confidence level is 1.96, the estimated proportion is 0.5, and the margin of error is 0.015.

Step 2 ：Calculate the sample size using the formula $n = \frac{Z^{2} \cdot p \cdot (1 - p)}{E^{2}}$ .

Step 3 ：Round up the result to the nearest integer to get the final sample size.

Step 4 ：The sample size needed to give a margin of error within $\pm 1.5 %$ in estimating a population proportion with 95% confidence is $4269$ .