The 112th Congress of the United States of America has 535 members, of which 87
ID: 3206639 • Letter: T
Question
The 112th Congress of the United States of America has 535 members, of which 87 are women. An alien lands near the US Capital and treats members of Congress as a random sample of the human race. He reports to his superiors the 95% confidence interval for the proportion of the human race that is female.
A) Calculate the confidence interval that the alien reports? Use the confidence interval for a proportion calculator
B) What is wrong with the alien's approach to estimating the proportion of the human race that is female
Explanation / Answer
A. The 95% c.i for true population proportion of female is as follows:
phat+-zalpha/2 sqrt[phat(1-phat)/n], where, phat is sample proportion, z denotes critical z score at alpha/2, and n is sample size.
=87/535+-1.96 sqrt[87/535(1-87/535)/535]
=0.1323, 0.1967
B. The alien wrongly assumed the 535 members of 112th Congress of the United States as random sample representative of human race, which wrongly led to calculation of sample proportion of female.
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