Home › AP Statistics › Statistics › Confidence Intervals › α is related to the confidence level CL by α + C…
α is related to the confidence level CL by α + CL = 1. What does α represent?
AThe probability the interval does contain the true parameter
BThe probability the interval fails to contain the true parameter
CThe margin of error itself, in decimal form
DThe sample size needed for a given confidence level
Answer & Solution
Correct answer: B. The probability the interval fails to contain the true parameter
1. CL is defined as the probability that a constructed confidence interval contains the true population parameter.
2. Since α + CL = 1, α is whatever probability is left over.
3. That leftover probability is exactly the chance the interval fails to capture the true parameter.
4. Option A describes CL itself, the complement of α, so it cannot also be the definition of α.
_Source: OpenStax Introductory Statistics (CC BY 4.0), Ch 8 "Confidence Intervals", section 8.1 A Single Population Mean using the Normal Distribution_
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