The population of incomes in a particular community is thought to be highly right-skewed with a mean equal to $36,789 and a standard deviation equal to $2,490. Based on this, if a sample of size n = 36 is selected, the sampling distribution would have a mean equal to the population mean, but the standard deviation of the sampling distribution will be one-sixth of the population standard deviation.

Question

Quizplus · Accepted Answer

The mean of the sampling distribution of the sample mean is equal to the population mean, and the standard deviation of the sampling distribution (standard error) is equal to the population standard deviation divided by the square root of the sample size, n. Here, sqrt(36) = 6, so the standard deviation of the sampling distribution is indeed one-sixth of the population standard deviation.

The Population of Incomes in a Particular Community Is Thought