AP Statistics: Unit 7 Chapter 27

Name: _________________________________________________ Date: _________________________________________ Period: ________Practice: Regression Inference Day 11. The Gallup organization has collected, over six decades, the data to the following question: “If your party nominated a generally well-qualified person for president who happened to be a woman, would you vote for that person?” The scatterplot of the data as well as the regression analysis are shown below.

a.) Explain in words and numbers what the regression equation states.

b.) State the hypothesis about the slope (both numerically and in words) that described how voters’ thoughts have changed about voting for a woman.

c.) Assuming that assumptions for inference are satisfied, perform the hypothesis test and state your conclusion. Be sure to state it in terms of the voters’ opinions.

d.) Explain what the R-squared in this regression means.

2. Here’s a regression of the percentage of respondents whose response to the question about the women president was “no opinion.” Has this position changed over the years? Assume that the conditions for inference are satisfied.

a.) State your hypothesis for the slope.

AP Statistics: Unit 7 Chapter 27

b.) Test your hypothesis and state your conclusion in proper context.

c.) Below is the scatterplot corresponding to the regression for No Opinion. How does that scatterplot change your opinion of the trend in “no opinion” responses? Do you think the true slope is negative? Does this change your conclusion of your hypothesis test of part (b)? Explain.

3. Does a person’s cholesterol level tend to increase with age? Data collected in Framingham, MA, from 294 adults aged 45 to 62 produced regression analysis shown. Assuming the data satisfy the conditions for inference, examine the association between age and cholesterol level by stating the appropriate hypothesis for the slope and your conclusion in the proper context.

4. The scatterplot suggests a decrease in the differences in ages at first marriage for men and women since 1975. We want to examine the regression to see if this decrease is significant.

a.) Write your hypotheses.

AP Statistics: Unit 7 Chapter 27

b.) The residual plot and histogram of the residuals is shown. Do you think the conditions for inference are satisfied? Explain.

c.) Test the hypothesis and state your conclusion about the trend in age at first marriage.

5. A consumer organization has reported test data for 50 car models. We will examine the association between weight of the car (in thousands of pounds) and the fuel efficiency (mpg). Shown are the summary statistics, scatterplot, and regression analysis.

Is there strong evidence of an association between the weight of a car and its gas mileage? Write the appropriate hypothesis. Do not perform the test or verify conditions. (Hey, there’s a first time for everything!)