For a population with N = 3, pi = 1/2, 1/3, 1/6 and yi = 7,5,2, two units are dr

Question

For a population with N = 3, pi = 1/2, 1/3, 1/6 and yi = 7,5,2, two units are drawn without replacement, the first with probability proportional to pi, the second with probability proportional to the remaining sizes. Verify that pi1 = 51/60, pi2 = 44/60, pi3 = 25/60 and pi12 = 35/60, pi13 = 16/60, pi23 = 9/60 For this method of sample selection, compare the variances of and and also compare them with the variance of using its method of sample selection. You may either construct all three possible estimates or use the variance formulas. Show that the ratio of of in sampling with replacement is close to the value 1/2 that applies for equal probability sampling Compute using two approaches construct all three possible estimates and the variance formula

Explanation / Answer

For sampling distribution we have the population of size N=3 Drawing sample of size 2 without replacement.

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