AP Statistics Flashcards: Justifying a Claim About the Slope of a Regression Model Based on a Confidence Interval
Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026
Review key ideas with interactive flashcards. This set includes 11 cards to help you master important concepts.
A researcher claims the true slope is 1.5. If the 99% confidence interval is (0.8, 2.5), is the researcher's claim plausible?
Yes, the claim is plausible because 1.5 is contained within the confidence interval of (0.8, 2.5), which provides the range of plausible values for the true slope.
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A researcher claims the true slope is 1.5. If the 99% confidence interval is (0.8, 2.5), is the researcher's claim plausible?
Yes, the claim is plausible because 1.5 is contained within the confidence interval of (0.8, 2.5), which provides the range of plausible values for the true slope.
What two key components must be referenced when interpreting a specific confidence interval for a slope?
An interpretation of a confidence interval for a slope must reference the sample from which it was calculated and the population parameter (true slope) it is estimating.
How does sample size affect the width of a confidence interval for the slope?
The width of the confidence interval for the slope tends to decrease as the sample size increases.
What is the general interpretation of a C% confidence interval in the context of repeated sampling for a regression slope?
In repeated sampling, approximately C% of confidence intervals created from samples of the same size will capture the true population regression slope.
How is a claim about the slope of a regression model justified using a confidence interval?
A claim is justified by checking if the value in the claim falls within the confidence interval, as the interval contains all plausible values for the true slope.
How would a confidence interval for the slope support a claim of *no linear association*?
If the confidence interval contains the value 0, it supports the claim of no linear association because a slope of 0 is a plausible value.
If a 95% confidence interval for a slope is (-0.5, 2.1), can you justify a claim of a positive linear relationship?
No, you cannot justify a claim of an exclusively positive relationship because the interval contains plausible values that are negative and zero.
What does a confidence interval for the slope of a regression model provide?
A confidence interval for the slope provides a range of plausible values for the true population regression slope that can be used to support a claim.
In the context of regression, what are 'plausible values'?
Plausible values are the range of values contained within a confidence interval that are considered reasonable estimates for the true population regression slope.
What is the primary purpose of constructing a confidence interval for the slope of a regression model?
Its primary purpose is to provide a range of plausible values for the true population slope, which can be used to justify a claim about the relationship between two variables.
Why does a larger sample size lead to a narrower confidence interval for the slope?
A larger sample size reduces sampling variability, which decreases the standard error of the slope and results in a narrower, more precise confidence interval.