Question

Among adults in the US, the distribution of albumin levels in cerebrospinal uid is roughly

symmetric with mean = 35mg=100ml and standard deviation = 10:1mg=100ml: Suppose

that you select repeated samples of size 30 from this population and calculate the mean for

each sample.

If you were to select a large number of random samples of size 30, the sample variance of

the means will be

a) approximately the same as population variance

b) larger than population variance

c) lower than population variance

Answer 1

Solution:

Correct option is

lower than population variance

Option c) is correct.

Explanation:

Solution:

Given that ,

=

Solution:

Given that ,

= 35mg

= 10:1mg

A sample of size n = 30 is taken from this population.

Let be the mean of sample.

The sampling distribution of the is approximately normal with

Mean = =

SD =      

So , Variance of means = =

n is the sample size which is always positive. n is at denominator

So ,    Variance of means is less than ²

Answer is

lower than population variance