AP Statistics Flashcards: Carrying Out a Test for the Slope of a Regression Model
Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026
Review key ideas with interactive flashcards. This set includes 14 cards to help you master important concepts.
What is the formula for the test statistic for the slope of a regression model?
The test statistic is calculated using the formula t = (b - beta) / SEb, where 'b' is the sample slope, 'beta' is the hypothesized population slope, and 'SEb' is the standard error of the slope.
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What is the formula for the test statistic for the slope of a regression model?
The test statistic is calculated using the formula t = (b - beta) / SEb, where 'b' is the sample slope, 'beta' is the hypothesized population slope, and 'SEb' is the standard error of the slope.
How does a significance test for slope provide justification for a claim about a population?
The test provides a p-value, which quantifies the strength of evidence against the null hypothesis, allowing a researcher to justify a claim about the population with statistical reasoning.
If a test for slope yields a low p-value (e.g., p < 0.05), what claim can be justified about the population?
A low p-value allows one to reject the null hypothesis and justify the claim that there is a statistically significant linear relationship between the variables in the population.
What is the formal decision rule used in a significance test for slope?
A formal decision is made by comparing the p-value to the significance level (alpha); if the p-value is less than or equal to alpha, we reject the null hypothesis.
What sampling distribution does the statistic t = (b - beta) / SEb follow?
The sampling distribution of the t-statistic for slope follows a t-distribution with n-2 degrees of freedom.
What fundamental assumption is made when interpreting a p-value for a test for slope?
The interpretation of a p-value for a test for slope assumes that the null hypothesis (which typically states the true population slope is zero) is true.
How are the degrees of freedom calculated for the t-distribution in a test for slope?
The degrees of freedom (df) for the t-distribution are calculated as df = n - 2, where 'n' is the sample size.
If you fail to reject the null hypothesis in a test for slope, what does this suggest about the relationship?
Failing to reject the null hypothesis means there is not convincing statistical evidence of a linear relationship between the two variables in the population.
What is the overall purpose of using the results of a significance test for slope?
The results provide the statistical reasoning needed to justify a claim and answer a research question about the relationship between two quantitative variables in a population.
A researcher conducts a test for slope and gets a p-value of 0.24. Using an alpha of 0.05, what conclusion should they make?
Since the p-value (0.24) is greater than alpha (0.05), the researcher should fail to reject the null hypothesis and conclude there is not convincing evidence of a linear relationship.
A p-value is compared to alpha to make a formal decision. What are the two possible outcomes of this comparison?
The two possible outcomes are to either reject the null hypothesis (if p-value ≤ alpha) or fail to reject the null hypothesis (if p-value > alpha).
In the context of a significance test for slope, what is an appropriate test statistic?
An appropriate test statistic for the slope of a regression model is the t-statistic, which measures how many standard errors the sample slope is from the hypothesized slope.
How do you interpret the p-value from a significance test for the slope?
Assuming the null hypothesis is true, the p-value is the probability of observing a sample slope as extreme or more extreme than the one actually observed.
What type of distribution is the null distribution for the slope of a regression model?
The null distribution for the slope of a regression model is a t-distribution.