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

Dolly Robinson

Dolly Robinson

Answered question


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.

Answer & Explanation



Skilled2021-08-24Added 83 answers

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
Now, we know that for large samples, the estimator hatp is approximately normal with mean p and standard deviation pqn where q=1p.
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^=1p^ is an estimator of  pqn.
Therefore, we have:
p^q^n=0.750.25400=0.022 Thus, 99% confidence limits for p are p^q^n=0.750.25400=0.022
Therefore, the 99% confidence interval for the population p is (0.69,0.80)=(69%,80%).
The confidence interval is (69%,80%).

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