Question

A certain population has a mean of 521 and a standard deviation of 33. Many samples of size 52 are randomly selected and the means calculated.

(a) What value would you expect to find for the mean of all these sample means? (Give your answer correct to nearest whole number.)

(b) What value would you expect to find for the standard deviation of all these sample means? (Give your answer correct to two decimal places.)

(c) What shape would you expect the distribution of all these sample means to have?

1) skewed right

2)approximately normal

3) skewed left

4) uniform

Answer 1

a)

sample mean is unbiased estimator of population mean

hence we expect the mean of all these sample means to be 521

b)

similarly

We expect the standard deviation of all these sample means = 33

c)

by central limit theorem

2) approximately normal