Question

Suppose 60% of the people in a country support a law. A group of people participate in a referendum about the law, and the law is passed if at least half of the participants vote in favor of the law. If the opinions are independent, what is the for which the law is passed with probability 99.9%?

Answer 1

Given that p = 0.6 lower limit of 99.9% C.I for p is p - z squareroot p (1 - p)/n greaterthanorequalto 0.5 0.6 - 3.091 squareroot 0.6 times 0.4/n greaterthanorequalto 0.5 Rightarrow 3.091 squareroot 0.6 times 0.4/n lessthanorequalto 0.1 Rightarrow n greaterthanorequalto [3.091/0.1]^2 times 0.6 times 0.4 n greaterthanorequalto 229.3 v minimum sample size = N = 230 v