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 = 67 inches and the standard deviation is σ =3.6 inches.

Suppose we randomly sample 98 values from this population and compute the mean, then repeat this sampling process 5000 times and record all the means we get.

Which of the following is the best approximation for the mean of our 5000 sample means?

1. 6.8
2. 98
3. 67

Answer 1

Solution:

= 67

= 3.6

Suppose we randomly sample 98 values from this population and compute the mean, then repeat this sampling process 5000 times and record all the means we get.

n = 98

Let denotes the sample mean

We have now 5000 values of

This is called as the sampling distribution of the sample mean.

This sampling distribution of is approximately normal with

Mean() =   

SD() =   

We have to find This is the mean of our all 5000 values of the sample means.

= = 67

So, answer is 67.