Question

Consider sampling heights from the population of all female college soccer players in the United States. Assume the mean height of female college soccer players in the United States is μ = 66 inches and the standard deviation is σ = 3.5 inches. Suppose we randomly sample 100 values from this population and compute the mean, then repeat this sampling process 5,000 times and record all the means we get.

Which of the following is the best approximation for the standard deviation of the 5,000 sample means?

A) .035
B) .35
C) 3.5

Answer 1

B) .35

Explanation:

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean
`\mu` and standard deviation
`\sigma`, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
`\mu` and standard deviation
`s = (\sigma)/(√(n))`.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem:

`\sigma = 3.5, n = 100`

Then

`s = (\sigma)/(√(n))`

`s = (3.5)/(√(100))`

`s = 0.35`

So the correct answer is:

B) .35