# chapter_27_answers_and_solutions - Chapter 27 Inferences...

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Chapter 27 Inferences for Regression 497 Chapter 27 – Inferences for Regression 1. Ms. President? a) The equation of the line of best fit for these data points is % ˆ .. ( ) Yes Year =− + 5 583 0 999 , where Year is measured in years since 1900. According to the linear model, the percentage of people willing to vote for a female candidate for president is increasing by about 1% each year. b) H 0 : There has been no change in the percentage of people willing to vote for a female candidate for president. β 1 0 = () H A : There has been a change in the percentage of people willing to vote for a female candidate for president. 1 0 c) Assuming the conditions have been met, the sampling distribution of the regression slope can be modeled by a Student’s t -model with (16 – 2) = 14 degrees of freedom. We will use a regression slope t -test. The value of t = 15.1. The P -value 0.0001 means that the association we see in the data is unlikely to occur by chance. We reject the null hypothesis, and conclude that there is strong evidence that the percentage of people willing to vote for a female presidential candidate is increasing. d) 94.2% of the variation in the percentage of people willing to vote for a female president is explained by the year. 2. Drug use. a) The equation of the line of best fit for these data points is % ˆ . . (% ) OtherDrugs Marijuana + 3 068 0 615 . According to the linear model, the percentage of ninth graders in these countries who use other drugs increases by about 0.615% for each additional 1% of ninth graders who use marijuana. b) H 0 : There is no linear relationship between marijuana use and use of other drugs. 1 0 = H A : There is a linear relationship between marijuana use and use of other drugs. 1 0 c) Assuming the conditions have been met, the sampling distribution of the regression slope can be modeled by a Student’s t -model with (11 – 2) = 9 degrees of freedom. We will use a regression slope t -test. The value of t = 7.85. The P -value of 0.0001 means that the association we see in the data is unlikely to occur by chance. We reject the null hypothesis, and conclude that there is strong evidence that the percentage of ninth graders who use other drugs is related to the percentage of ninth graders who use marijuana. Countries with a high percentage of ninth graders using marijuana tend to have a high percentage of ninth graders using other drugs. d) 87.3% of the variation in the percentage of ninth graders using other drugs can be accounted for by the percentage of ninth graders using marijuana.

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498 Part VII Inference When Variables are Related e) The use of other drugs is associated with marijuana use, but there is no proof of a cause-and-effect relationship between the two variables. There may be lurking variables present. 3. No opinion. a) H 0 : There has been no change in the percentage of people expressing no opinion about their willingness to vote for a female candidate for president.
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