Home › AP Statistics › Statistics › Confidence Intervals › What adjustment does the 'plus four' method make…
What adjustment does the 'plus four' method make to a proportion confidence interval, and why is it applied?
AIt multiplies the sample size by four for extra precision
BIt adds two successes and two failures to correct estimation error
CIt subtracts four observations to remove outliers
DIt always adds four percentage points to the final interval
Answer & Solution
Correct answer: B. It adds two successes and two failures to correct estimation error
1. Estimating the standard deviation of a proportion from p' and q' alone can introduce error, especially with small samples.
2. The plus-four adjustment imagines four extra trials, two additional successes and two additional failures.
3. This changes the working sample size to n+4 and the working success count to x+2 before the usual formula is applied.
4. Options C and D invent operations, subtracting observations or adding fixed percentage points, that this method never performs.
_Source: OpenStax Introductory Statistics (CC BY 4.0), Ch 8 "Confidence Intervals", section 8.3 A Population Proportion_
Related questions
A campus survey wants to estimate, with 95% confidence and a margin of error no greater thIn a Zogby poll of 48 respondents, nine rated a terrorist attack in their community as likOf 511 southern California homes surveyed for earthquake preparedness, 338 did NOT meet miContinuing the Field Poll example, p' = 0.79 from 400 of 506 surveyed. For a 90% confidencA Field Poll finds that 400 out of 506 surveyed California adults, about 79%, feel educatiAt the Ice Chalet, a randomly selected beginning skating class of 80 children has 64 girlsA poll of 1,200 voters finds 65% name the economy as the most significant election issue. A survey of 200 households finds that in 120 of them, the woman makes the majority of purc