Question

Suppose a large population has a mean μand standard deviation σ, and a simple randomsample of size nis taken. The sampling distribution of the sample mean xhas mean andvariance respectively equal to(a)μ/nand σ2/n.(b)μand σ/n.(c)μ/nand σ2/n2.(d)μand σ2/n.

Answer 1

(d) μ and σ²/n

Explanation:

In a sampling distribution of sample means, the mean is equal to the population mean, which is μ.

The standard deviation of the sampling distribution of sample means is given by

σ/√n.

The variance of a distribution is the square of the standard deviation; this means the variance of the sampling distribution of sample means would be

(σ/√n)² = σ²/(√n)² = σ²/n