Suppose a large population has mean μ and standard deviation σ, and a simple random sample of size n is taken. What are the mean and variance, respectively, of the sampling distribution of the sample mean x̄?

Question

Quizplus · Accepted Answer

The mean of the sampling distribution of the sample mean ($x̄$) is equal to the population mean ($\mu$), and the variance of the sampling distribution of the sample mean is equal to the population variance ($\sigma^2$) divided by the sample size ($n$), hence $\sigma^2 / n$. However, since variance is $\sigma^2$, the standard deviation (which is the square root of variance) of the sampling distribution is $\sigma / \sqrt{n}$.

Suppose a Large Population Has Mean μ and Standard Deviation