BASIC PRAC OF STATISTICS+LAUNCHPAD+REE
BASIC PRAC OF STATISTICS+LAUNCHPAD+REE
8th Edition
ISBN: 9781319123680
Author: Moore
Publisher: MAC HIGHER
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Chapter 6, Problem 6.25E

a.

To determine

To make: A two-way table showing defendant’s race and death penalty.

a.

Expert Solution
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Answer to Problem 6.25E

The two-way table of defendant’s race and death penalty is given below:

  Defendant’s Race
  White Black
Death 19 17
No death 141 149

Explanation of Solution

Given info:

The data show the 326 cases where the defendant was sentenced for committing murder. The results are tabulated below:

White defendant:

  White Victim Black Victim
Death 19 0
No death 132 9
Total 151 9

Black defendant:

  White Victim Black Victim
Death 11 6
No death 52 97
Total 63 103

Calculation:

The total number of deaths and no death committed by white defendant is given below:

  White Victim Black Victim Total
Death 19 0 19
No death 132 9 141

Table 1

The total number of deaths and no death committed by black defendant is given below:

  White Victim Black Victim Total
Death 11 6 17
No death 52 97 149

Table 2

Thus, combing the totals obtained in Table 1 and Table 2 gives the two-way table for defendants and death penalty.

  Defendant’s Race
  White Black
Death 19 17
No death 141 149

Justification:

The two-way table is obtained by adding the values under each row of the two tables for white and black defendants.

b.

To determine

To show: The Simpson paradox holds good for the given two-way table.

b.

Expert Solution
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Answer to Problem 6.25E

The Simpson paradox holds good for the given two-way table.

Explanation of Solution

Calculation:

The percentage of black victim given death sentence under white defendant table is calculated as follows:

(Percentage of black victimgiven death sentence underwhite defendant)=(Number of black victims givendeath sentence under white defendant)(Total number of black victimsunder white defendant)×100=09×100=0

Thus, none of the black victims is sentenced to death under white defendant.

The percentage of black victims given death sentence under black defendant table is calculated as follows:

(Percentage of black victimgiven death sentence underblack defendant)=(Number of black victims given deathsentence under black defendant)(Total number of black victimsunder black defendant)×100=6103×100=0.06×100=6

Thus, 6% of the black victim is sentenced to death under black defendant.

The percentage of white victim given death sentence under white defendant table is calculated as follows:

(Percentage of white victimgiven death sentence underwhite defendant)=(Number of white victims given deathsentence under white defendant)(Total number of white victimunder white defendant)×100=19151×100=0.126×100=12.6%

Thus, 12.6% of the white victim is sentenced to death under white defendant.

The percentage of white victims given death sentence under black defendant table is calculated as follows:

(Percentage of white victimgiven death sentence underblack defendant)=(Number of white victims given deathsentence under black defendant)(Total number of white victimunder black defendant)×100=1163×100=0.175×100=17.5

Thus, 17.5% of the white victim is sentenced to death under black defendant.

The percentage of death sentence given to white defendant is calculated as follows:

(Percentage of deathamong white defendants)=(Number of death for white defendantsTotal number of white defendants)×100=19160×100=0.119×100=11.9

Thus, 11.9% of death sentence was given to white defendant.

The percentage of death sentence given to black defendant is calculated as follows:

(Percentag of deathamong black defendants)=(Number of death for black defendantsTotal number of black defendants)×100=17166×100=0.102×100=10.2

Thus, 10.2% of death sentence was given to black defendant.

The percentages of deaths under the white defendant and black defendant are given below:

  Defendant’s Race
  White Black
Death 11.9% 10.2%

The individual percentage of deaths under white victims and black victims is given below:

  White Victim Black Victim
Death for White defendant 12.6% 0
Death for Black defendant 17.5% 6%

Thus, the Simpson's paradox is proved.2

c.

To determine

To explain: The existence of Simpson’s paradox for the given data to a judge.

c.

Expert Solution
Check Mark

Answer to Problem 6.25E

The death penalty was assigned mainly for the cases involving white victims, which is 14% of cases with a white victim and 5.4% of cases with a black victim. Also, most of the white defendants are white victims, and cases having white victims have additional risk of death penalty, white defendants are being assigned the death penalty more overall.

Explanation of Solution

Calculation:

For white defendants, the percentage of white victims is calculated as follows:

(Percentage of white victimsunder white defendants)=(Number of white victims given death sentence+Number of white victims given no death sentence)Total number of white defendants×100=(19+13219+132+0+9)×100=151160×100=94.4

Thus, 94.4% of white victims are under white defendants.

For black defendants, the percentage of white victims is calculated as follows:

(Percentage of white victimsunder black defendants)=(Number of white victims given death sentence+Number of white victims given no death sentence)Total number of black defendants×100=(11+5211+52+6+97)×100=63166×100=37.95

Thus, 37.95% of white victims are under black defendants.

The overall death penalty involving white and black victims are calculated as follows:

White defendant:

  White Victim Black Victim
Death 19 0
No death 132 9
Total 151 9

Black defendant:

  White Victim Black Victim
Death 11 6
No death 52 97
Total 63 103

Adding the corresponding columns of white victim and black victim

  White Victim Black Victim
Death 19+11=30 0+6=6
Total 151+63=214 9+103=112

The percentage of cases involving white victims is given below:

(Percentage of casesinvolving white victims) =30214×100=0.14×100=14%

Thus, the percentage of cases involving white victims is 14%.

The percentage of cases black victims is given below:

(Percentage of casesinvolving black victims) =6112×100=0.054×100=5.4%

Thus, the percentage of cases involving black victims is 5.4%.

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