1. Give an example of two numeric variables that you believe would be strongly correlated. Give a brief explanation for your answer. 2. Give an example of two numeric variables that you believe would be uncorrelated. Give a brief explanation for your answer. 3. Give an example of two numeric variables that you believe would be positively correlated. Give a brief explanation for your answer. 4. Give an example of two numeric variables that you believe would be negatively correlated. Give a brief explanation for your answer. 1. (Hypothetical) From a previous study, the registered voters in a particular district were 48% Republican, 41% Democrat and 11% independent. Prior to the most recent election, a random sample of 150 voters showed 64 Republicans, 58 Democrats, and 28 independents. Is there enough evidence to suggest that the distribution among registered voters has changed since the previous study? Use a 0.05 level of significance. a. Hypotheses b. Expected counts c. Test statistic d. p-value e. Conclusion 2. To test the effectiveness of a new drug, a researcher gives one group of individuals the new drug and another group a placebo. Using a x2 test at a 0.1 level of significance, determine if the researcher can conclude that the drug is effective? Medication Drug Placebo Effective 32 12 Not effective 9 18 a. Hypotheses b. Expected counts c. Test statistic d. p-value e. Conclusion 3. A teaching assistant gives a quiz with ten questions and no partial credit. After grading papers, the TA writes down for each student the number of questions that student got right and the number wrong. The average number of right answers is 6.4 with a SD of 2.0; the average number of wrong answers is 3.6 with the same SD of 2.0. The correlation between the number of right answers and the number of wrong answers is: 0 -0.50 0.50 -1 1 can't tell without data Explain: 1. (Hypothetical) The following information was obtained from a study of car maintenance: Age of car (in years); X=8 and SDx=3 Cost in annual maint./repairs ($): Y =190 and SDy=60 Correlation: R=0.8 Assume X and Y are approximately normally distributed. A) For a car that is nine (9) years old, what annual maint./repair cost is predicted? B) Skip C) What is the regression equation for predicting the annual maintenance/repair cost given age of the car? 2. Suppose for a sample of students, the average number of hours they work out per week is 6.89 with a standard deviation of 5.66. I also asked them to rank themselves based on athleticism. 10 means more athletic than the rest of the students in the class and 1 means less athletic than the rest of the students in the class. For the athleticism ranking, the average is 6.4 with a standard deviation of 2.4. The correlation coefficient between these two variables is 0.319. a. Predict the ranking a student would give themselves if they worked out 2 hours per week. b. Predict the ranking a student would give themselves if they worked out 10 hours per week. c. Calculate the root mean square for the data. d. For an individual that is in the 90th percentile for hours worked out in a week, what percentile are they in for ranking based on athleticism? e. Calculate the regression equation for the data