9.1 EXERCISES SECTION 9.1 Correlation 481 For Extra Help: MyLab® Statistics Building Basic Skills and Vocabulary 1. Two variables have a positive linear correlation. Does the dependent variable increase or decrease as the independent variable increases? What if the variables have a negative linear correlation? 2. Describe the range of values for the correlation coefficient. 3. What does the sample correlation coefficient r measure? Which value indicates a stronger correlation: r = 0.918 or r = -0.932? Explain your reasoning. 4. Give examples of two variables that have perfect positive linear correlation and two variables that have perfect negative linear correlation. 5. Explain how to determine whether a sample correlation coefficient indicates that the population correlation coefficient is significant. 6. Discuss the difference between r and r. 7. What are the null and alternate hypotheses for a two-tailed t-test for the population correlation coefficient r? When do you reject the null hypothesis? 8. In your own words, what does it mean to say “correlation does not imply causation”? List a pair of variables that have correlation but no cause-and-effect relationship. In Exercises 9 and 10, identify the explanatory variable and the response variable. 9. A nutritionist wants to determine whether the amounts of water consumed each day by persons of the same weight and on the same diet can be used to predict individual weight loss. 10. An actuary at an insurance company wants to determine whether the number of hours of safety driving classes can be used to predict the number of driving accidents for each driver. Graphical Analysis In Exercises 11–14, determine whether there is a perfect positive linear correlation, a strong positive linear correlation, a perfect negative linear correlation, a strong negative linear correlation, or no linear correlation between the variables. 11. x y 12. x y 13. x y 14. x y
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