Question

4. Many realistic applications involve sampling without replacement. For example, in manufacturing, quality control inspectors sample items from a finite production run without replacement. For such a finite population, we have to

adjust the value of σ(X). Take (without replacement) samples of size 2 from the above population of N= 5 objects {1, 2, 3, 4, 5}

(1,2) (1,3) (1,4) (1,5) (2,3), (2,4), (2,5)................ ______________________________________________________

a. How many such samples are possible?

b. List all the X ’s, i.e. the means of all these samples of size 2 _______________________________________________________

c. Find the mean of these means, i.e. E(X) d. Is E(X)=μ?

e. Find the standard errorσ(X), i.e. the std. deviation of all these means

2

f. Show that the standard error equals

Note: N − n is called the finite population correction factor. Typically it is N −1

used when the sample size n is greater than 5% of the finite population size.

Answer 1

solution:

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