Chapter 1.1, Problem 35E

(a)

To determine

To make: A two-way table of defendant’s race versus death penalty.

Answer to Problem 35E

	Death Penalty	Total
	Yes	No
Black Defendants	$17$	$149$	$166$
White Defendants	$19$	$141$	$160$
Total	$36$	$290$	$326$

Explanation of Solution

Given:

White Defendant
White	Black
Victim	Victim

Death	$19$	$0$
Not	$132$	$9$

Black Defendant
White	Black
Victim	Victim

Death	$11$	$6$
Not	$52$	$97$

From the given data, we construct a two way table of defendant’s race(white or black) versus death penalty (yes or no) as shown below.

	Death Penalty	Total
	Yes	No
Black Defendants	$17$	$149$	$166$
White Defendants	$19$	$141$	$160$
Total	$36$	$290$	$326$

Conclusion:

Therefore, a two-way table is drawn.

(b)

To determine

To Find: Show that Simpson’s paradox holds

Answer to Problem 35E

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

Explanation of Solution

From the data below Simpson’s paradox holds because $11.875\%$ of while defendants have got death penalty as compare to $10.24\%$ of black defendants and $14\%$ or white victims and $5.36\%$ of black victims have been given death penalty.

	Black Defendants	White defendants
	Number	$\%$	Number	$\%$
Death	$17$	$10.24096$	$19$	$11.875$
Not	$149$	$89.75904$	$141$	$88.125$
Total	$166$	$100$	$160$	$100$

	White Defendants	Black defendants
	Number	$\%$	Number	$\%$
Death	$30$	$14.01869159$	$6$	$5.357142857$
Not	$184$	$85.98130841$	$106$	$94.64285714$
Total	$214$	$100$	$112$	$100$

Conclusion:

Therefore, Simpson’s paradox holds because $11.875\%$ of while defendants have got

(c)

To determine

To explain: why the paradox holds in language

Answer to Problem 35E

Black Victims or black Defendants have less percentage of death penalty as compare to white victims and white defendants.

Explanation of Solution

In case of White Victims , $14\%$ have got death penalty.

In case of White Defendants, $11.86\%$ have got death penalty.

In case of Black Victims, $5.36\%$ have got death penalty.

In case of Black Defendants, $10.24\%$ have got death penalty.

Overall, Black Victims or black Defendants have less percentage of death penalty as compare to white victims and white defendants.