1. Worksheet Sampling and Bivaritate 1.A survey was conducted in the United States and 10 countries of Western Europe to determine if marijuana use increased the likelihood of using other drugs. The percentage of teenagers who had used marijuana and other drugs are summarized below.

2. a) Construct a scatter plot of these data. Describe what the scatter plot tells us about the data (answer in terms of strength and direction) Marijuana Use(%) Other Drugs (%) R = 0.9340985

3. a) Construct a scatter plot of these data. Describe what the scatter plot tells us about the data (answer in terms of strength and direction) The scatter plot tells us that there is a strong positive relationship between Marijuana use in teens and the use of other drugs in teens.

4. b) Calculate the equation of the least-squares regression line. Describe the meaning of the slope and the intercept in the context of the problem. The equation of the least-squares regression line is y = 0.615x - 3.0678 The slope (0.615) is the amount of change in the percentage of use of other drugs per one percentage point change in marijuana use. The intercept (-3.0678) indicates that in a country with no marijuana use among teens, there is less than no use of other drugs. Since that in impossible, there must be other factors that contribute to teen use of other drugs.

5. c) Calculate the correlation coefficient and the coefficient of determination and describe what they mean in the context of the problem. The correlation coefficient is R = 0.9340985 An R value that close to 1 means that this relationship between teen marijuana use and teen use of other drugs is close to linear. The coefficient of determination is R² = 0.87254 A value that close to 1 means that most of the variation of the percentage of teens using other drugs can be explained by the variation of the percentage of teens that use marijuana.

6. d) Sketch a residual plot and describe what it tells you about the model. Write the values of the ordered pairs below. Marijuana Use(%) Other Drugs (%)

7. d) Sketch a residual plot and describe what it tells you about the model. Write the values of the ordered pairs below. Marijuana UseActual Other Drug Use – Predicted ODU 22-6.4622 17-4.3872 40-0.5322 50.9928 37-3.6872 19-0.6172 232.9228 62.3778 71.7628 531.4728 346.1578

8. Worksheet Sampling and Bivaritate 2.) A guidance counselor conducts a study to determine the effect of caloric intake at breakfast on alertness in first-period classes. She interviews an SRS of 20 students who claim to eat under 1,000 calories at breakfast, and an SRS of 20 students who claim to eat over 1,000 calories at breakfast. In each group, she measures alertness on a standard scientific scale.

9. a) Explain why this is an observational study and not an experiment. This is an observational study because there is no change in behavior. The physiologist simply measures the claimed breakfast caloric intake and energy level.

10. b) Give an example of a possible confounding variable with an explanation in the context of the study. Sleep patterns Weight and Size Activity level in the morning Time of test

11. c) If the students who eat over 1,000 calories test higher on the alertness scale, is it reasonable to encourage all students to eat larger breakfasts? No reasonable – Correlation does not mean causation

12. d) How could the counselor design a related experiment to study caloric intake at breakfast with alertness in first period? Random groups Serve each group breakfast – Double Blind To minimize confounding variables – Same morning activities