AP Statistics Flashcards: Justifying a Claim Based on a Confidence Interval for a Difference of Population Proportions
Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026
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When is the value '0' of special significance in a confidence interval for a difference of proportions?
If '0' is a plausible value within the interval, we cannot justify a claim of a difference between the two population proportions.
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When is the value '0' of special significance in a confidence interval for a difference of proportions?
If '0' is a plausible value within the interval, we cannot justify a claim of a difference between the two population proportions.
A 95% confidence interval for the difference in proportions (p1 - p2) is (-0.04, 0.10). Can we claim there is a difference between the two population proportions?
No, a claim of a difference cannot be justified because the interval contains 0, making it a plausible value for the true difference.
If a confidence interval for the difference in the proportion of voters favoring a candidate in two districts is (0.02, 0.08), what claim is supported?
Since the entire interval of plausible values is positive, it supports the claim that the proportion in the first population is greater than in the second.
What is the primary purpose of a confidence interval for a difference in proportions?
It provides an interval of plausible values for the true difference in population proportions, which can be used to support or justify a claim.
A researcher interprets an interval for a difference in proportions of students who pass an exam between two schools. What populations should be referenced?
The interpretation should reference the larger populations of all students at each of the two schools from which the samples were drawn.
What does the confidence level (C%) mean in the context of repeated sampling?
It means that in repeated sampling, approximately C% of the constructed confidence intervals will capture the true difference in population proportions.
How does a confidence interval for a difference of proportions help in justifying a claim?
The interval provides a range of plausible values; if all values in the interval support a claim (e.g., are all positive), the claim is justified.
Define 'plausible values' in the context of a confidence interval for a difference of proportions.
Plausible values are the range of estimates within the confidence interval that are considered reasonable for the true difference between the two population proportions.
How do you justify a claim that two population proportions are different based on a confidence interval?
The claim is justified if the confidence interval for the difference in proportions does not contain 0, as this indicates 0 is not a plausible value.
What two key components must be referenced when interpreting a confidence interval for a difference in proportions?
The interpretation must reference both the samples from which the data were collected and the populations to which the inference is being made.