AP®︎ Statistics: Topic 3.11 Flashcards
Master key terms and definitions for Topic 3.11 of AP Statistics – Justifying a Claim Based on a Confidence Interval for the Difference Between Two Population Proportions to help you prep for quizzes and the AP exam.
Parameter for a Two-Proportion Confidence Interval
p₁ − p₂, the true difference between two population proportions
p₁ − p₂, the true difference between two population proportions
An interval for p₁ − p₂ must be interpreted in that order; reversing to p₂ − p₁ reverses the signs of the endpoints
We are C% confident that the interval from a to b contains the true difference p₁ − p₂, where p₁ and p₂ are the population proportions for the two groups in context
In repeated random sampling with the same sample sizes from the same populations, about C% of confidence intervals produced by this method will contain the true difference p₁ − p₂
Values inside the confidence interval are plausible for p₁ − p₂ at that confidence level; values outside are not
Provides convincing evidence that p₁ > p₂, so the population proportions differ
Provides convincing evidence that p₁ < p₂, so the population proportions differ
If the interval contains 0, there is insufficient evidence to conclude that the two population proportions differ
If 0 is in the interval, equality is plausible, but the data do not provide convincing evidence that p₁ = p₂
If 0 is an endpoint, the interval contains 0, so there is still insufficient evidence of a difference
A claim such as p₁ − p₂ > k is supported only if the entire interval is greater than k
If a proposed value for p₁ − p₂ is in the interval, it is a plausible value; if it is outside, the interval provides evidence against it
A difference such as 0.10 in proportions means 10 percentage points, not necessarily a 10 percent increase
With independent random samples, conclusions can be generalized to the populations from which the samples were selected, not automatically to broader groups
With samples from two existing groups, the interval can support that the population proportions differ, but not that group membership caused the difference
In a randomized experiment, the interval can support a cause-and-effect conclusion about the treatments; generalization still depends on how the units were selected
Includes the confidence level, that the interval contains the true difference p₁ − p₂, the two populations, the response/success, and the order of subtraction, all in context
The interval estimates only p₁ − p₂; it does not separately locate p₁ and p₂ and does not estimate a ratio such as p₁/p₂
Because the interval is based on random samples, any one computed interval either contains the true difference p₁ − p₂ or it does not
