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Stat 332 Sampling and Experimental Design (Due 1229pm before class, Friday, Oct 19, 2012) Assignment 2 1. In the upcoming US presidential election this November, Florida is a key swing state that is very authoritative in determining the outcome. Currently the give outicipatory expectation Barack Obama and the Republi chamberpot candidate Mitt Romney be virtually tied in recent polls. For this question, you can use 9 million as our universe size this is just about the centre itemize votes in the 2008 presidential election in Florida. a) The in style(p) poll asked 890 likely voters and found that the proportion of Florida residents likely to vote for the Democratic candidate is 47%, construct a 95% con? dence detachment for this estimate under(a) the SRSWOR. By the way, the support for Republican is 46%, and the easing are undecided. (b) If a news organization wants to conduct a SRSWOR travel along to ? nd out the theatrical role of Florida residents supporting the Democr atic candidate, what is the sample size needed to achieve a dissolver which is accurate within 0. percentage point, 19 out 20 times? 2. We have 120 students in Stat332. (a) What is the total number of possible samples of size 10 under SRSWOR? (b) think that among the 120 students of Stat332, 60 are masculine students and 60 are feminine students. We want to perform a STSRS (strati? ed simple random sampling) with male students and female students being two strata, and we want to survey 5 students from for each one stratum, what is the total number of possible samples? What is the ratio of the two numbers (STSRS/SRSWOR)? 3. Lohr (2010) Ch3, Q10 part a.Hard shell scar may be sampled by using a dredge. Clams do not tend to be uniformly distributed in a body of water, however, as some areas provide better home ground than others. Thus, taking a simple random sample is likely to result in a large estimated variant for the number of clams in an area. Russell (1972) used strati? ed random sampling to estimate the total number of bushels of hard shell clams (Mercenaria mercenaria) in Narragansett Bay, Rhode Island. The area of interest was divided up into four strata based on preliminary surveys that identi? d areas in which clams were abundant. Then nh dredge tows were made in stratum h, for h = 1, 2, 3, 4. The land area for each stratum was known, and Russell calculated that the area ? shed during a measuring rod dredge tow was 0. 039 acres, so that we may use Nh = 25. 6 ? Areah . hither are the results from the survey taken before the commercial season. Estimate the total number of bushels of clams in the area, and give the standard error of your estimate. horizontal surface 1 2 3 4 Area Number of (Acres) Tows make 222. 81 4 49. 61 6 50. 25 3 197. 1 5 Average Number of Sample Variance Bushels per Tow for story 0. 44 0. 068 1. 17 0. 042 3. 92 2. 146 1. 80 0. 794 4. Assume the sample variance in Q3 is a good estimate for the strata variance, and we want a strati? ed sample size of n = 21. (a) Calculate the stratum sample sizes under proportional allocation. (b) Calculate the stratum sample sizes under optimal (Neyman) allocation. (c) What are the values (approximately) of V (? st ) with sample size allocations of (a) and y (b), respectively? equality these two variances and comment. . Foresters want to estimate the average age of trees in a stand. Determining age is cumbersome, because one needs to count the tree peal on a core taken from the tree. In general, though, the older the tree, the larger the diameter, and diameter is easy to measure. The foresters measure the diameter of all 1132 trees and ? nd that the population mean equals 10. 3. They then randomly select 20 trees for age measurement. The info can be downloaded as hw2q5. txt from course website on Waterloo Learn and pronounce into R using d