Question

Suppose we are interested in estimating the proportion p of a population that has a certain disease. As in Section 2.3 let y;-1 if person i has the disease, and yi 0 if person i does not have the disease. Then p . a Show, using the definition in (2.13), that 22 N- np If the population is large and the sampling fraction is small, so that write (2.26) in terms of the CV for a sample of size 1. N-1 FIGURE 2.6 Histogram of the means of 1000 samples of size 300, taken with replacement from the data in Example 2.5. 200 150 100 50 0 240,000 280,000 320,000 360,000 Estimated Sampling Distribution of y b Suppose that the fpc 1. Consider populations with p taking the successive values 0.001,0.005, 0.01, 0.05,0.10, 0.30, 0.50, 0.70,0.90, 0.95, 0.99,0.995,0.999. For each value of p, find the sample size needed to estimate the population pro portion (a) with fixed margin of error 0.03, using (2.25), and (b) with relative error 0.03p, using (2.26). What happens to the sample sizes for small values of p?

Answer 1

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