AP Statistics Flashcards: Setting Up 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 10 cards to help you master important concepts.
What are the four conditions that must be verified before conducting a significance test for a regression slope?
The four conditions are that the relationship is linear, the standard deviation of y is constant, the data are independent, and the responses are normal for each x value.
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What are the four conditions that must be verified before conducting a significance test for a regression slope?
The four conditions are that the relationship is linear, the standard deviation of y is constant, the data are independent, and the responses are normal for each x value.
A researcher wants to determine if there is *any* linear relationship between a student's height and their test score. What would the null and two-sided alternative hypotheses be?
The null hypothesis would be H0: β = 0, and the two-sided alternative hypothesis would be Ha: β ≠ 0.
What is the appropriate statistical test for the slope of a regression model?
The appropriate test for the slope of a regression model is a t-test for a slope.
What is the 'Independent' condition for a regression slope test?
The 'Independent' condition requires that individual observations in the dataset are independent of each other.
What is the 'Normal' condition for a regression slope test?
The 'Normal' condition requires that for any fixed value of x, the corresponding responses in y are normally distributed.
What is the 'Equal Standard Deviation' condition for a regression slope test?
This condition requires that the standard deviation of the response variable (y) is the same for all values of the explanatory variable (x).
If you want to test whether a new fertilizer has a positive effect on crop yield (slope > 0), what kind of alternative hypothesis should you use?
You should use a one-sided alternative hypothesis, specifically Ha: β > 0, to test for a positive relationship.
What are the three primary steps to set up a significance test for the slope of a regression model?
The three steps are to identify the appropriate test method, define the null and alternative hypotheses, and verify the necessary conditions for inference.
What is the general form of the null hypothesis (H0) for a t-test for a slope?
The null hypothesis for a t-test for a slope is H0: β = β0, where β0 is the hypothesized value of the slope, which is often zero.
What is the 'Linear' condition for a regression slope test?
The 'Linear' condition requires that the true relationship between the explanatory (x) and response (y) variables is linear.