2 points) The male female sex ratio in a certain species is unknown. Let p denot

Question

2 points) The male female sex ratio in a certain species is unknown. Let p denote the probability that a randomly selected individual is female. Choose a sample of n people and estimate the probability p by Sn/n, where Sn is the number of females in the sample. (a) If n 2500, find the smallest e such that p is in the interval (Sn/n - e, Sn/n+e) with probability at least 0.87 (b) At least how large should the sample size n be so that the estimate Sn/n is within 0.032 of the true value with probability at least 0.98? HINT: I Sn Bin(n, p), then P(-e

Explanation / Answer

a)for no prior information estimated proportion p=0.5

n=2500; std error =(p(1-p)/n)1/2 =0.01

here for 86% confidence level ; critical value of z =1.51

hence margin of error =E =z*std error = 1.51 * 0.01 = 0.015

b)

for margin of error E =0.032

and for 98% CI ; z = 2.33

therefore required sample size n=p(1-p)*(z/E)2 = 1325.4150

Sample size is approximately = 1325

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