Noting that the critical z-value for a 95% confidence interval for a proportion is almost equal to 2, it
can be seen that the required sample size is approximately equal to the reciprocal of the squared desired
margin of error.

Question

Quizplus · Accepted Answer

The statement is true. The critical z-value for a 95% confidence interval is 1.96, which is nearly equal to 2. The formula for calculating the sample size for a proportion is n = (z^2 * p * q) / E^2 where z is the critical value, p is the estimated proportion, q is 1-p, and E is the desired margin of error. Rearranging this formula, we get E^2 = (z^2 * p * q) / n. Since z is approximately equal to 2, the reciprocal of the squared desired margin of error is approximately equal to the sample size needed, which supports the statement.

Noting That the Critical Z-Value for a 95% Confidence Interval