Question

.Table below is a 2 × 2 table from an article that studied effects of racial characteristics on whether persons convicted of homicide received the death penalty. The 674 subjects classified in the table were the defendants in indictments involving cases with multiple murders in Florida between 1976 and 1987. Is there enough evidence that the death penalty was imposed less often on black defendants than on white defendants?

     

		Death Penalty
		Yes	No	TOTAL
Defendant’s Race	White	53	430	483
	Black	15	176	191
	TOTAL	68	606	674

Answer 1

Result:

Table below is a 2 × 2 table from an article that studied effects of racial characteristics on whether persons convicted of homicide received the death penalty. The 674 subjects classified in the table were the defendants in indictments involving cases with multiple murders in Florida between 1976 and 1987. Is there enough evidence that the death penalty was imposed less often on black defendants than on white defendants?

     

	Death Penalty
		Yes	No	TOTAL
Defendant’s Race	White	53	430	483
	Black	15	176	191
	TOTAL	68	606	674

Group1 = White

Group2 = Black

Two sample proportion test used

Ho: P1 = P2   H1: P1 > P2

Upper tail test used

p1=53/483=0.1097

p2=15/191=0.0785

P = (x1+x2)/(n1+n2)

=(53+15)/(483+191) = 0.1009

=1.2118

Table value of z at 0.05 level = 1.645

Rejection Region: Reject Ho if z > 1.645

Calculated z = 1.2118 not in the rejection region

The null hypothesis is not rejected.

There is not enough evidence to conclude that the death penalty was imposed less often on black defendants than on white defendants.

Z Test for Differences in Two Proportions
Data
Hypothesized Difference	0
Level of Significance	0.05
Group 1
Number of Items of Interest	53
Sample Size	483
Group 2
Number of Items of Interest	15
Sample Size	191
Intermediate Calculations
Group 1 Proportion	0.1097
Group 2 Proportion	0.0785
Difference in Two Proportions	0.0312
Average Proportion	0.1009
Z Test Statistic	1.2118
Upper-Tail Test
Upper Critical Value	1.645
p-Value	0.1128
Do not reject the null hypothesis