Suppose we are analyzing an election in which a fraction p of the voters support

Question

Suppose we are analyzing an election in which a fraction p of the voters support one candidate, and a fraction 1 - p of the voters support the other candidate. Let X ¯ denote the fraction of respondents to a poll who supported the first candidate, and let Y ¯ = 1 - X ¯ denote the fraction of respondents to the same poll who supported the other candidate. The margin between the two candidates is the difference between the fractions of voters that support them.

i) What is the standard deviation of the estimated margin?

Let a denote the width of a confidence interval for the margin, let b denote the width of a confidence interval for the first candidate, and let c denote the width of a confidence interval for the second candidate.

(i) What is a/b?
(ii) What is b/c?

Explanation / Answer

Suppose we are analyzing an election in which a fraction p of the voters support one candidate, and a fraction 1 - p of the voters support the other candidate. Let X ¯ denote the fraction of respondents to a poll who supported the first candidate, and let Y ¯ = 1 - X ¯ denote the fraction of respondents to the same poll who supported the other candidate. The margin between the two candidates is the difference between the fractions of voters that support them. i) What is the standard deviation of the estimated margin? Two candidates one candidate has fraction p of the voters support and other candidate has fraction 1-p of the voters support Mean of the candidates is 2-p and standard deviation is sqrt((4-3p)-(2-p)^2)

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