Which statistic is the standard deviation of the sampling distribution of the sample proportion?

Which statistic is the standard deviation of the sampling distribution of the sample proportion?

• A. Standard error of the proportion
• B. Standard error of the mean
• C. Standard deviation of the population
• D. Confidence interval for the mean

Answer: (A)

The standard deviation of the sampling distribution of a sample proportion is called the standard error of the proportion. It measures how much p-hat would vary across many samples of size n from the same population, and for a proportion it equals sqrt(p(1-p)/n) (using p-hat if p is unknown). The other concepts describe different ideas: the standard error of the mean concerns the sampling distribution of the sample mean; the standard deviation of the population is a fixed population parameter, not a measure of sampling variability; and a confidence interval for the mean is an interval estimate that uses the standard error, not the standard deviation itself.

The standard deviation of the sampling distribution of a sample proportion is called the standard error of the proportion. It measures how much p-hat would vary across many samples of size n from the same population, and for a proportion it equals sqrt(p(1-p)/n) (using p-hat if p is unknown). The other concepts describe different ideas: the standard error of the mean concerns the sampling distribution of the sample mean; the standard deviation of the population is a fixed population parameter, not a measure of sampling variability; and a confidence interval for the mean is an interval estimate that uses the standard error, not the standard deviation itself.