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Statistics 651: Survey Sampling Methods Winter 2011 Practice Problems for Exam 2 Solutions 1. Nursery Workers (a) This is stratified random sampling followed by a single stage cluster sample. The probability that any one worker is selected can be calculated: ij = P(worker selected | nursery selected)P(nursery selected) = 1 n h N h Thus, for each of the strata, the weight of every worker in that stratum is N h n h , as shown in this table: State N h n h weight = N h /n n AZ 243 20 12.15000 TN 1383 23 60.13043 RI 87 2 43.50000 DE 131 10 13.10000 OH 1434 32 44.81250 MI 1525 12 127.08333 IN 437 10 43.70000 FL 7703 30 256.76667 (b) With the further subsampling, the probability of selection now becomes: ij = P(worker selected | nursery selected)P(nursery selected) = m ih M ih n h N h Thus, the weight is w ij = N h M ih n h m ih . For the first nursery: w ij = 87 21 2 10 = 91 . 35 For the second nursery: w ij = 87 34 2 10 = 147 . 9 Note that the weight increased over 43.5 for both nurseries, and it increased more for the larger nursery. This is because the 10 people selected from the larger nursery need to represent more people than the 10 people from the smaller nursery. 2. Lockhart City (a) I used the SAS program using sampling probability proportional to size. First, I read the data from figure A2 into SAS, and then I used SURVEYSELECT with PPS, and SIZE = number of households in the county. I have chosen districts 51, 71, 62, 65, and 63. 1 (b) P(select household ij on first draw) = P(select household j on first draw | Cluster i selected on first draw) P(Cluster i selected on first draw) = 1 M i M i K = 1 K = 1 19664 . (c) Yes. (d) Variance Estimates and CIs (calculated in R): i. deff = 3. Ignoring the fpc for the SRS sample, V ( SRS ) = 0 . 19 V ( Complex ) = deff * V ( SRS ) = 3 * . 19 = 0 . 575 95% CI: 11 . 047 1 . 96 . 575 = (9 . 55 , 12 . 54) 2... View Full Document