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dorumonsg

Member

Registered: 2009-09-12

Posts: 1

Sampling Distribution

Supposing I have 4 numbers, 0, 2, 4 and 6. I pick any 2 random numbers with replacement which gives me...

0 2
0 4
0 6
2 4
2 6
4 6
0 0
2 2
4 4
6 6

I assume the permuatations of the numbers don't matter, I am picking samples afterall, why would it matter?

So I want to find the Sampling Standard Deviation for these 10 sets of numbers, the correct answer given is SquareRoot of 5/SquareRoot of 2

Which means Population Variance should be 10 if we work backwards, given the formula for Standard Deviation of Sampling Distribution :
1/(n^2) * Population Variance, judging from the given answer n should be 2. Which gives the Population Variance as 5/2 divided by 1/(2^2) which is 10.

Problem is I can't find this 10... or rather I don't know the proper way. I've been trying to use 1/20(Sum of x^2 - [(Sum of x)^2]/20), I also tried  1/20(Sum of x^2 - [(Sum of x)^2]/2) but I didn't get 10... okay ignore what I tried... just try it your own way I am probably wrong to kingdom come... I've been staring at this question for 13 hours already...

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Oh I think I just found the answer, but I would like to clarify stuff. I think I got the formulas messed up.

Here's what I did I took the Population Variance : 1/20 (Sum of (xi^2...+ zi^2) - Sum of (xi... + zi)^2/20). Basically, I took 20 because there are a total of 20 numbers in the 10 sets of 2. And I know the entire population so I did not use n-1. Which gives me 5.

So for Sampling Distribution Variance is Population Variance/n, so n is 2 as each sample consist of 2 numbers. so 5/2 is the variance.

I probably got confused because I didn't know what number is n... so I would like to clarify am I right to say :

1) Sampling Distribution Variance is Population Variance/n where n = the sample size(The number of variables in 1 set of sample regardless how many samples you have.) For example, you have 3 samples, Sample 1 {A, B}, Sample 2 {B, C}, Sample 3 {C, D}. the sample size is 2 even though you have 3 sets and a total of 6 variables.

2) As for the population variance n is the total number of variables you have regardless of Sample Size. For example, for Sample 1 {A, B}, Sample 2 {B, C}, Sample 3 {C, D}, n would be 6 as there is 6 variables, even though we have only 3 sets.

3) Which means to the n for Population Variance and the Variance of Sampling Distribution is a different n? I got confused because the formula I have had the 2 n in the same formula and I though they have to be the same.

Once this is clarify, I can move on. Am I right?

Last edited by dorumonsg (2009-09-12 16:00:08)