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.

Determine the correlation coefficient between the number of cases filed and the percentage of guilty pleas.

-.441202 or about -.44

What can you say about the degree of association between these two variables for these data?

The relationship is negative and relatively weak. There is an indication that when one of the variables is high, the other tends to be low.

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?

You could easily argue either way on this one. It is a surprise since we don't expect young persons to have high cholesterol.

On the other hand, people who watch a lot of TV tend not to get much exercise and maybe that makes them unhealthy.

(b) Do you think watching television causes higher cholesterol levels?

It is one thing to say they are related...but quite another to say that TV watching CAUSES high cholesterol. association is not causation.

(c) Do you think the reverse is true: high cholesterol levels make young adults more likely to watch television?

Sure, why not, there is nothing to stop you from making the reverse argument here but once again, is one thing to say they are related...but association is NOT causation.

(d) How would you explain the results of this study?

Think back to your readings on experiments and observational studies. What kind of study do you think this is. Sounds like an observation study. Many other things could be going on here, for example, maybe young adults who watch a lot of television also tend to be at home and sick...so their cholesterol could be high for reasons other than TV watching.