Question

Suppose we want to estimate the mean weight gain among a cohort of
college freshmen. We randomly sample 324 freshmen and follow them over
the entirety of their first year. Unknown to us, in the entire cohort, the mean
weight gain over the year is 20 pounds and the standard deviation is 9 pounds.
What is the expected value and the standard error of the sample mean?

Answer 1

Let X be the weight gain among a cohort of college freshmen.

Given the mean weight gain and standard deviation is

We randomly sample 324 freshmen.

According to central limit theorem as sample size(n) becomes sufficiently large the distribution of sample mean is approximately normal with mean and Standard deviation

Therefore the expected value of sample mean is

and standard error is



hence the standard error of the sample mean is 0.50