Principle, a distribution of means

Question

1) In principal, a distribution of means can be formed by

A) calculating the mean of all the possible samples of a given size and dividing it by the variance.

B) using the sample's mean and variance divided by the population's parameters.

C) randomly estimating the population variance from the various samples of the same size, and using the sample mean in place of μ.

D) randomly taking a very large number of samples from a population, each of the same size, and making a distribution of their means.

Answer 1

Theresa:

 

A quick note:  The second word should be spelled principle.

 

Answer (D)  comes closest to the correct answer.  The correct answer is:

 

In principle the sampling distribution of sample means can be formed by considering all possible samples of the given size from the population, calculating the sample mean for each and every possible sample and making a distribution of these sample means.

 

Theresa, if suppose you were interested in sampling distribution of the square of the sample median, you would say, 

 

In principle the sampling distribution of squares of sample medians can be formed by considering all possible samples of the given size from the population, calculating the square of the sample median for each and every possible sample and making a distribution of these squares of sample medians.

 

Every statistic ( quantity you can compute from the sample) ahs a sampling distribution which can be thought  of as in the above manner.

 

Dr. G.