- Assume pps (probability proportional to size) with replacement sampling of size n from a finite population of size N, where pi is the per-draw selection probability of the i-th unit in the population and pi is proportional to a measure of size Xi.
1.1 On the j-th draw of sampling (for j = 1, …,n), what is the probability of not selecting unit i?
1.2 Find the probability of never selecting unit i on any of the n draws.
1.3 Find the probability of selecting unit i at least once.
- Assume srs wor (simply random sampling without replacement). We are interested in estimating the mean of a characteristic y. Assume S2 = 10, 000 is an advance estimate of variability, and r = .8 is an advance estimate of the response rate. How large should the sample be if the half-width of the standard confidence interval (95 percent) is to be less than 10?
- We are interested in conducting a survey to estimate a population proportion P. Assume srs wor (simple random sampling without replacement), p’ = 0.20 is an advance estimate of the population proportion, and r = .67 is an advance estimate of the response rate. How large should the sample be if the half-width of the standard confidence interval (95 percent) is to be less than 0.05?