The male:female sex ratio in a certain species is unknown. Let pp denote the pro

Question

The male:female sex ratio in a certain species is unknown. Let pp denote the probability that a randomly selected individual is female.
Choose a sample of n people and estimate the probability pp by Sn/n, where SnSn is the number of females in the sample.
(a) If n=8000n=8000, find the smallest such that pp is in the interval (Sn/n,Sn/n+) with probability at least 0.86.

(b) At least how large should the sample size nn be so that the estimate Sn/n is within 0.03 of the true value with probability at least 0.9

Explanation / Answer

a)for no prior information estimated proportion p=0.5

n=8000; std error =(p(1-p)/n)1/2 =0.0056

here for 86% confidence level ; critical value of z =1.4758

hence margin of error =E =z*std error =0.0082

b)

for margin of error E =0.03

and for 90% CI ; z =1.6449

therefore required sample size n=p(1-p)*(z/E)2 =~ 752

please revert for any clarification required

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