Chapter 12, Problem AP4.40CPT

To determine

To find out which of the following does not support the conclusion that being a Republican and favoring the death penalty are not independent.

Answer to Problem AP4.40CPT

Option (b) is the correct option.

Explanation of Solution

“Republican” and “Favoring” the death penalty are independent if the proportion of republicans among those who favor the death penalty is the same as the proportion of Republicans in the entire sample. We note that $299$ of the Republicans favor the death penalty while there are $494$ people in the sample that favored the death penalty. Thus, the proportion of republicansamong tose those who favor the death penalty is:

  $\frac{299}{494}=0.6053$

We note that $397$ of the people in the sample are republicans while there are are $850$ people in the sample. Thus, the proportion of republicans in the sample is:

  $\frac{397}{850}=0.4671$

Since the two proportion are not the same, thus,

  $\frac{299}{494}\ne \frac{397}{850}$

Thus, option (b) is the correct option.