The standard error of the sampling distribution of sample proportion, SE( ), depends on the value of the population proportion, p, and the closer the value of p to 0.50, the larger SE( ) will be for a given sample size n.

Question

The standard error of the sampling distribution of sample proportion, SE(  ), depends on the value of the population proportion, p, and the closer the value of p to 0.50, the larger SE(  ) will be for a given sample size n.

Quizplus · Accepted Answer

This is true because the formula for the standard error of the sampling distribution of sample proportion is SE = sqrt[(p*(1-p))/n]. As p approaches 0.50, the denominator (p*(1-p)) approaches its maximum value, and therefore the whole formula approaches its maximum value, resulting in a larger standard error.

The Standard Error of the Sampling Distribution of Sample Proportion