Two Correlation Problems for practice
1. The following data relate the number of criminal cases filed in various US cities to the percentage of those cases that result in a plea of guilty.
|
City |
% resulting in a guilty plea |
number of cases filed |
|
San Diego, CA |
73 |
11534 |
|
Dallas, TX |
72 |
14784 |
|
Portland, OR |
62 |
3892 |
|
Chicago, IL |
41 |
35528 |
|
Denver, CO |
68 |
3772 |
|
Philadelphia, PA |
26 |
13796 |
|
Lansing, MI |
68 |
1358 |
|
St. Louis, MO |
63 |
3649 |
|
Davenport, IA |
60 |
1312 |
|
Tallahassee, FL |
50 |
2879 |
|
Salt Lake City, UT |
61 |
2745 |
Determine the correlation coefficient between the number of cases filed and the percentage of guilty pleas.
What can you say about the degree of association between these two variables for these data?
2. A recent observation study has found a strong positive correlation (i.e. an r > .5) between the cholesterol levels of young adults and the amounts of time they spend watching television.
(a) Would you have expected such a result? Why?
(b) Do you think watching television causes higher cholesterol levels?
(c) Do you think the reverse is true: high cholesterol levels make young adults more
likely to watch television?
(d) How would you explain the results of this study?