← Statistics syllabus

United StatesStatistics

Unit 9: Inference for Quantitative Data: Slopes

6 dot points across 6 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

How do you compute the t test statistic and P-value and conclude a test about a regression slope?

Topic 9.5 Carrying Out a Test for the Slope of a Regression Model: compute the t test statistic for the slope using the standard error, find the P-value with n minus 2 degrees of freedom, and state a conclusion in context.
A focused answer to AP Statistics Topic 9.5, on computing the slope t statistic from the sample slope and its standard error, finding the P-value with n minus 2 degrees of freedom, and concluding in context, with a full worked test from regression output.
11 min answer →

How do you construct a confidence interval for the slope of a regression model?

Topic 9.2 Confidence Intervals for the Slope of a Regression Model: check the regression conditions and construct a t-interval for the population slope using the sample slope, its standard error, and n minus 2 degrees of freedom.
A focused answer to AP Statistics Topic 9.2, on building a t-interval for the population slope - checking the regression conditions, reading the slope and its standard error from computer output, and using n minus 2 degrees of freedom - with a full worked interval.
11 min answer →

Why is the slope of a least-squares regression line a statistic with its own sampling distribution, and what does that allow us to infer?

Topic 9.1 Introducing Statistics: Do Those Points Align?: explain why a sample regression slope varies from sample to sample, motivating inference about the true population slope of a linear model.
A focused answer to AP Statistics Topic 9.1, on why a sample regression slope is a statistic that varies across samples, motivating confidence intervals and tests about the true population slope of a linear model.
9 min answer →

How do you use a confidence interval for a regression slope to justify a claim about the relationship?

Topic 9.3 Justifying a Claim About the Slope of a Regression Model Based on a Confidence Interval: use a slope interval to judge whether a linear relationship exists and to evaluate claims about the size and direction of the slope.
A focused answer to AP Statistics Topic 9.3, on using a regression-slope confidence interval to judge whether a linear relationship exists and to assess claims about the size and direction of the slope, with worked justifications.
9 min answer →

How do you choose the correct inference procedure across all of the course's procedures for a given scenario?

Topic 9.6 Skills Focus: Selecting an Appropriate Inference Procedure: choose the correct inference procedure (proportion, mean, chi-square, or slope; interval or test; one or two samples; paired or independent) for any scenario across the whole course.
A focused answer to AP Statistics Topic 9.6, on choosing the correct inference procedure across the entire course - proportion, mean, chi-square, or slope; interval or test; one or two samples; paired or independent - based on the scenario, with a worked decision.
11 min answer →

How do you state the hypotheses and check the conditions for a significance test about a regression slope?

Topic 9.4 Setting Up a Test for the Slope of a Regression Model: state the null and alternative hypotheses about the population slope, identify the significance level, and verify the regression conditions for a t-test.
A focused answer to AP Statistics Topic 9.4, on writing the null and alternative hypotheses for a regression slope (testing beta equals 0), choosing the significance level, and checking the regression conditions for a t-test.
9 min answer →