Mr. Kram is considering running for mayor of the land of the dawn. Before completing the petitions, he decided to conduct a survey of voters in the land of dawn. A sample of 400 voters reveals that 300 would support him in the May Election. Develop a 99 percent confidence interval for the population proportion.

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SchulzD · Accepted Answer

Let a random sample of size n=400 voters reveals that m=300 would support him n the May Election. Then, m/n gives an estimate of the unknown proportion p. Denote the estimator of p by p^,i.e.,p^=mn Therefore the value of hatp is p^=mn=34=0.75 Now, we know that for large samples, the estimator hatp is approximately normal with mean p and standard deviation pqn where q=1−p. In practice p is unknown and we are concerned with estimation of p. The standard deviation pqn is unknown then and has to be estimated. The statistic p^q^n where p^=mn,q^=1−p^ is an estimator of  pqn. Therefore, we have: p^q^n=0.75⋅0.25400=0.022 Thus, 99% confidence limits for p are p^q^n=0.75⋅0.25400=0.022 Therefore, the 99% confidence interval for the population p is (0.69,0.80)=(69%,80%). The confidence interval is (69%,80%).

Mr. Kram is considering running for mayor of the land of the dawn.

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