Question

Among adults in the US, the distribution of albumin levels in cerebrospinal fluid is roughly symmetric with mean µ = 50mg/100ml and standard deviation σ = 12.7mg/100ml. Suppose that you select repeated samples of size 20 from this population and calculate the mean for each sample. If you were to select a large number of random samples of size 20, the sample variance of the means will be

a) larger than population variance

b) approximately the same as population variance

c) lower than population variance

Answer 1

Solution:

Correct option is

c) lower than population variance

Explanation:

Given that ,

= 50

= 12.7

A sample of size n = 20 is taken from this population.

Let be the mean of sample.

The sampling distribution of the is approximately normal with

Mean = = 50

SD =      = 12.7/​20 = 2.8398

2.8398 < 12.7

<  

<  ²

Correct option is

c) lower than population variance