Define the standard error of the proportion.

• A. The standard deviation of the individual values around the mean
• B. The standard deviation of the sampling distribution of the proportion
• C. The variance of the population proportion
• D. The mean of the sampling distribution of the proportion

Answer: (B)

The standard error of the proportion is the standard deviation of the sampling distribution of the proportion. When many samples of size n are drawn from a population with true proportion p, the sample proportions p-hat vary from sample to sample. This variability is captured by the standard error, which equals sqrt(p(1-p)/n). In practice, p is unknown, so we estimate it with p-hat and use sqrt(p-hat(1-p-hat)/n) as the estimate of the standard error. This measure reflects how precise a single sample’s proportion is as an estimate of the true population proportion and decreases as the sample size grows. It’s about the spread of the estimator across repeated samples, not the dispersion of individual values or the population variance or the mean of the sampling distribution.