Q 35. - The Practice of Statistics for AP

Question

Race and the death penalty Whether a convicted murderer gets the death penalty seems to be influenced by the race of the victim. Here are data on

$326$ cases in which the defendant was convicted of murder:

(a) Use these data to make a two-way table of the defendant’s race (white or black) versus the death penalty (yes or no).

(b) Show that Simpson’s paradox holds: a higher percent of white defendants are sentenced to death overall, but for both black and white victims a higher percent of black defendants are sentenced to death.

(c) Use the data to explain why the paradox holds in the language that a judge could understand.

Step-by-Step Solution

Answer

Part (b) Simpson’s paradox holds because $11.875\%$ of while defendants have got.

Part (c) When compared to white victims and white defendants, black victims and black defendants face a lower percentage of the death penalty.

Part (a) The two-way table is 

	Death penalty	Total
	Yes	No
Black defendants	17	149	166
White defendants	19	141	160
Total	36	290	326

Part(a) Step 1: Given information

Given data : 

	White defendants	Black defendants
	White victim                           Black victim	White victim                    Black victim
Death	19                                               0	11                                          6
Not	132                                             9	52                                       97

Part (a) Step 2: Concept

Data concerning two categorical variables are organized in a two-way table of counts. Two-way tables are frequently used to summarize vast volumes of data by categorizing outcomes.

Part (a) Step 3: Explanation

We create a two-way table comparing the defendant's race (white or black) vs. the death penalty (yes or no) using the data provided, as shown below. A two-way table is generated as a result. 

	Death penalty	Total
	Yes	No
Black defendants	17	149	166
White defendants	19	141	160
Total	36	290	326

Part (b) Step 1: Calculation

According to the data below, $11.875$ percent of white defendants have received the death penalty, while $10.24$ percent of black defendants have received the death penalty, and $14$ percent of white victims and $5.36$ percent of black victims have received the death penalty.  As a result, Simpson’s paradox holds because $11.875\%$ of while defendants have got. 

	Black defendants	White defendants
	No.	%	Number	%
Death	17	10.24096	19	11.875
Not	149	89.75904	141	88.125
Total	166	100	160	100

	White defendants	Black defendants
	No.	%	Number	%
Death	30	14.01869159	6	5.357142857
Not	184	85.98130841	106	94.64285714
Total	214	100	112	100

Part (c) Step 1: Calculation

In the instance of White Victims, $14\%$ were sentenced to death. 11.86 percent of white defendants have received the death penalty. $5.36$percent of black victims have received the death penalty. $10.24$ percent of black defendants have received the death penalty. When compared to white victims and white defendants, black victims and black defendants receive a lower percentage of the death penalty.