Assignment:
Question 1. Ester is an epidemiologist and body builder She is planning a survey of Chicago area body builders to determine the proportion who have ever used anabolic steroids. Her sampling frame consists of membership lists obtained from all accredited health clubs in the six county Chicago metro area. She has stratified clubs into the following three groups on the basis of their clientele:
1. Inner city yuppie
2. Inner city blue collar
3. Suburban.
She anticipates that the proportion using steroids will be twice as high in stratum 1, which contains most of the "hard-core" competitors as in stratum 2, and that the proportion in stratum 3 will be about two-thirds as high as that in stratum 2. From her membership lists, she enumerates 8345 members in stratum 1. 5286 in stratum 2, and 6300 in strata 3. If she can sample 1000 persons, how many should be allocated to each stratum? (Assume overall proportion using steroids is 12%)
Question 2. Ester is able to obtain $25,000 from BBAAS to conduct her survey. This will be her only source of funding. She estimates that it would cost $30 per interview in strata 1 and 2, and $40 per interview in stratum 3. With this in mind, how many persons should she interview in each stratum?
Question 3. Ester feels that it would only be worthwhile to do her survey if she can 95% certain of estimating the rate to within 15% of its true value. She anticipates that the overall rate will be about 12%. Based on her funding level indicated in previous problem, does she have enough funds to meet her specifications?
Provide complete and step by step solution for the question and show calculations and use formulas.