The size of the standard error of the sample proportion is dependent on the value of the population proportion and the closer the population proportion is to .50, the larger the standard error for a given sample size will be.

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The standard error of the sample proportion is calculated as sqrt[p(1-p)/n], where p is the population proportion and n is the sample size. The formula shows that the standard error is largest when p is 0.5, as the product p(1-p) reaches its maximum value at this point, making the standard error larger for a given sample size.

The Size of the Standard Error of the Sample Proportion