We wish to estimate the number of nests on a group of 40 islands. The total area of the islands is 100 hectares.

a) We sample with probability proportional to size (area) with replacement. (We want a sample of size 3.) How do we do this?

b) When will this sampling approach give us a really small variance?

c) Why not just take a SRS of islands? Would this give an unbiased estimator?

d) If we get the following values, estimate the total number of nests. (Dont use the general Horvitz-Thompson formula. You could, but you dont want to?)

e) BONUS: Compute the se of the estimate and give a 95 percent confidence interval for the number of nests. Also, it will turn out that the se is relatively low. What feature of the data shows you that this approach will be efficient? f) What are the assumptions of the estimator you used?

Area NestCount

(ha)

2 40

4 85

6 115