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In a Zogby poll of 48 respondents, nine rated a terrorist attack in their community as likely or very likely. The standard proportion tools cover confidence intervals for a single sample proportion like this one. What quantity would the 'plus four' method add to this raw count of nine before building a confidence interval?
ATwo, bringing the working success count to 11
BFour, bringing the working success count to 13
CNine, doubling the working success count to 18
DZero, since plus four never changes the success count
Answer & Solution
Correct answer: A. Two, bringing the working success count to 11
1. The plus-four method always adds exactly two extra successes and two extra failures to the raw counts.
2. Starting from x = 9 successes, the working success count becomes x + 2 = 11.
3. The working sample size becomes n + 4 = 52, not just the success count.
4. Option B adds all four observations to the success count alone, which misapplies the two-and-two split the method actually uses.
_Source: OpenStax Introductory Statistics (CC BY 4.0), Ch 8 "Confidence Intervals", section 8.3 A Population Proportion_
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