AP Statistics Flashcards: Justifying a Claim Based on a Confidence Interval for a Population Proportion
Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026
Review key ideas with interactive flashcards. This set includes 21 cards to help you master important concepts.
If you want a higher level of confidence for an interval calculated from the same sample, what will happen to the margin of error?
The margin of error will increase. For a given sample, the width of the confidence interval, which is directly related to the margin of error, increases as the confidence level increases.
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If you want a higher level of confidence for an interval calculated from the same sample, what will happen to the margin of error?
The margin of error will increase. For a given sample, the width of the confidence interval, which is directly related to the margin of error, increases as the confidence level increases.
A researcher calculates a 90% confidence interval to be [0.21, 0.29]. Can they conclude that the true population proportion is definitely within this range?
No, they cannot be certain. A confidence interval either contains the population proportion or it does not; the confidence level applies to the long-run process, not a single interval.
What does it mean to be "C% confident" that an interval captures the population proportion?
It means that if we were to take many samples and create many intervals, approximately C% of those confidence intervals would capture the true population proportion.
Why is it incorrect to say, "There is a 95% probability that the true population proportion is in the interval [0.4, 0.5]"?
This is incorrect because any single confidence interval either contains the population proportion or it does not. The 95% refers to the success rate of the method in repeated sampling, not a single interval.
What is the primary purpose of interpreting a confidence interval?
The primary purpose is to state the interval of plausible values for the true population proportion based on the sample data.
What two key elements must be included when interpreting a confidence interval for a population proportion?
An interpretation must include a reference to the sample from which the interval was calculated and the population it represents.
For a given sample, how does increasing the confidence level affect the width of the confidence interval?
For a given sample, the width of the confidence interval increases as the confidence level increases.
What is the relationship between the width of a confidence interval and its margin of error?
The width of a confidence interval is exactly twice the margin of error.
Identify the relationship between sample size, confidence interval width, and confidence level.
Increasing sample size decreases interval width, while increasing the confidence level increases interval width.
A poll's 99% confidence interval for a candidate's support is [0.48, 0.54]. A rival claims the candidate has less than majority support (p < 0.50). Is this claim plausible?
Yes, the rival's claim is plausible. The confidence interval contains values less than 0.50, providing a range of plausible values that may support the claim.
Explain the trade-off between confidence level and the width of a confidence interval.
To be more confident that an interval captures the true proportion, the interval must be wider. As the confidence level increases, the width of the interval also increases.
If you want to decrease the margin of error without changing the confidence level, what should you do to the sample size?
You should increase the sample size, as the width of a confidence interval, which is twice the margin of error, tends to decrease as sample size increases.
What is the fundamental truth about any single, calculated confidence interval regarding the population proportion?
A single confidence interval either contains the true population proportion or it does not.
How does increasing the sample size affect the width of a confidence interval?
The width of a confidence interval tends to decrease as the sample size increases.
How is a confidence interval used to justify a claim about a population proportion?
If the claimed value for the population proportion falls within the calculated confidence interval, the claim is considered plausible because the interval contains plausible values.
A 95% confidence interval for the proportion of defective widgets is [0.02, 0.06]. The company claims that less than 1% of widgets are defective. Is this claim supported by the interval?
No, the claim is not supported by the interval. The value 0.01 is not within the interval of plausible values, [0.02, 0.06].
Define the "confidence level" (C%) in the context of repeated sampling.
In repeated sampling, approximately C% of the confidence intervals created from the samples will successfully capture the true population proportion.
A researcher wants to create a narrower confidence interval than their last one while using the same confidence level. What must they change about their sampling method?
They must increase their sample size. The width of a confidence interval tends to decrease as sample size increases.
A 90% confidence interval for the proportion of adults who own a pet is [0.58, 0.64]. How would you interpret this interval?
We are 90% confident that the interval from 0.58 to 0.64 captures the true proportion of all adults in the population who own a pet.
What does a confidence interval for a population proportion provide?
A confidence interval provides an interval of plausible values for the true population proportion.
A 95% confidence interval for the proportion of voters supporting a candidate is [0.52, 0.58]. Is the claim that the candidate has majority support (p > 0.50) plausible?
Yes, the claim is plausible because the entire interval of plausible values is above 0.50, which supports the claim.