Statistics: Slope - Confidence Interval and Hypothesis Test

Objectives

• Students will be able to identify the conditions that need to be met to perform inference procedures for the slope of a regression line.
• Students will be able to interpret the results of a hypothesis test for slope and write the conclusion in context.
• Students will be able to calculate the degrees of freedom for inference procedures on bivariate data.
• Students will be able to interpret a confidence interval for the slope in context.

Vocabulary

• bivariate data
• confidence interval
• degrees of freedom
• hypothesis test for slope
• least-squares regression
• normal probability plot
• p-value
• residual
• scatterplot
• slope

About the Lesson

This lesson involves investigating the confidence interval and hypothesis test for the slope of a regression line.
As a result, students will:

• Check the conditions for inference for slope by inspecting a scatterplot of the data, the normal probability plot, and a plot of the residuals.
• Write the appropriate null and alternative hypotheses for the given scenario, determine the degrees of freedom for the data, and interpret the results of a hypothesis test for the slope.
• Analyze the results of a hypothesis test performed on the TI-Nspire, make a decision to reject or fail to reject the null hypothesis, and write their conclusion in the context of the situation.
• Calculate and interpret a confidence interval in context.
• Compare the information they get about the relationship from a hypothesis test and from a confidence interval.