## Elementary statistics

**This test is due in class on Monday, December 6. **

Questions 1-5 are worth 2 points each. Circle the best answer. Justification is not required.

1. The stronger the linear relationship between paired-sample data X and Y, the closer the
correlation coefficient is to +1 or -1. True
2. Suppose you calculate the correlation coefficient r between temperature X and volume Y. Then
you recalculate, using Celsius instead of Fahrenheit for X. Will the value of the correlation

coefficient

**r** change?

Yes

3. Suppose statisticians determined that there is a significant positive correlation between gun
ownership and violent crime. Does this prove that guns

**cause** violent crime?

Yes

4. Suppose that you found that the correlation coefficient between X and Y is

**r** = -0.568 and you

determined that the critical value for the correlation coefficient at the 5% significance level in Table A-6 is .444. Are X and Y significantly correlated? Yes
5. The variables X and Y in the following scatter plot have a positive correlation coefficient.

**The remaining questions are worth 4 points each. Show your work for complete and partial **

credit. Work carefully, especially with data entry into lists and/or matrices.
Questions 6 and 7: The paired data below consist of the test scores of four randomly selected Math 142 students and the numbers of hours they studied for this test.
6. What is the value of the correlation coefficient

**r**. How did you get your answer?

7. What percentage of the variation in test score is explained by the number of hours studied?
Questions 8-11: Refer to Data Set 16 in Appendix B and use the amounts of fat and the measured calorie counts.
8. Construct a scatterplot using amounts of fat on the x-axis and calories on the y-axis. 9. Are fat and calories significantly correlated at the 5% significance level? Why or why not?
10. Find the equation of the regression line using amounts of fat on the x-axis and calories on the y-
11. Find the best predicted calorie count for a cereal with 0.05 grams of fat per gram of cereal. Questions 12 and 13:
State Farm Insurance Co. claims that fatal car crashes occur with equal
frequency each day of the week. You have gathered the following data:
12. How many fatalities would you expect each day of the week if State Farm is correct in their
13. At the 0.05 significance level, test State Farm’s claim. Justify your answer.
The cholesterol-reducing drug Lipitor contains a calcium additive. Some
clinicians believe that the additive can cause headaches. The contingency table below shows the number of patients who experienced and did not experience headaches broken down by the amount of Lipitor they received (based on data from Parke-Davis).
14. Assuming that getting a headache or not is independent of the amount of Lipitor received,
calculate the expected frequencies for each of the cells of the table and fill in the table below. For at least one cell, show how to calculate the expected frequency.
15. Use a 0.05 significance level to test the claim that getting a headache is independent of the
amount of Lipitor received. Justify your answer.

Source: http://voyager.dvc.edu/faculty/dmurphy/Math142/Unit5TakeHomeTest.pdf

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