(Due: 12:29pm 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 important in determining the outcome. Currently the Democratic candidate Barack Obama and the Republican candidate Mitt Romney are virtually tied in recent polls. For this question, you can use 9 million as our population size; this is approximately the total number votes in the 2008 presidential election in Florida. (a) The latest 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% conﬁdence interval for this estimate under the SRSWOR.

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2. We have 120 students in Stat332. (a) What is the total number of possible samples of size 10 under SRSWOR? (b) Suppose that among the 120 students of Stat332, 60 are male students and 60 are female students. We want to perform a STSRS (stratiﬁed simple random sampling) with male students and female students being two strata, and we want to survey 5 students from each 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 clams 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 habitat than others. Thus, taking a simple random sample is likely to result in a large estimated variance for the number of clams in an area. Russell (1972) used stratiﬁed 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 into four strata based on preliminary surveys that identiﬁed areas in which clams were abundant. Then nh dredge tows were made in stratum h, for h = 1, 2, 3, 4. The acreage for each stratum was known, and Russell