Quiz 5ReviewName:

Standard(s) assessed / Score
17.Categorical variable distributions
  • Compute and interpret conditional and marginal distributions

18.Segmented Bar Graphs
  • Create and interpret segmented bar graphs

19.Categorical Variable Relationships
  • Describe the relationship between two variables (categorical v categorical)
  • Apply the concept of relative risk
  • Determine whether 2 categorical variables are independent
  • Understand Simpson's Paradox - Level 1 only

The table below, from the DeathPenaltyInformationCenter, summarizes the executions carried out in the US from 1976 through Sept 24, 1999.

EXECUTIONS
1996 - 1999 / Black
Victim / White
Victim / total
Black Defendant / 64 / 137
White Defendant / 10 / 315
total

a.What proportion of Black Victims (in percents) were

murdered by a Black Defendent? White Defendant?

b.Find the conditional distribution of defendants for murdering a white victim.

c.Using your calculations in a. and b. show a visual comparison of the conditional distributions in a segmented bar graph.

  1. The variables VICTIM and DEFENDANT are not independent. Describe the relationship between these two variables supporting your conclusions with appropriate calculations.

e. Using the totals computed above, fill in the empty cells in such a way that the two variables will be independent.

EXECUTIONS
1996 – 1999 / Black
Victim / White
Victim / total
Black Defendant
White Defendant
total

f.A 1998 study entitled The Death Penalty in Black and White examined the sentences following 665 murder convictions in Philadelphia courts between 1983 and 1993. This table shows how many death sentences were given among all the murder convictions.

Black Defendant

DEATH
SENTENCES / Black
Victim / White
Victim / Total
Death Penalty / 76 / 21 / 97
Not / 346 / 78 / 424
Total / 422 / 99 / 521

White Defendant

DEATH
SENTENCES / Black
Victim / White
Victim / Total
Death Penalty / 1 / 17 / 18
Not / 24 / 104 / 128
Total / 25 / 121 / 146

g.Of all black defendants convicted of murder, what proportion were sentenced to death?

h.Of all white defendants convicted of murder, what proportion were sentenced to death?

i.What proportion of black defendants convicted for murdering a black victim were sentenced to death?

j.What proportion of white defendants convicted for murdering a black victim were sentenced to death?

e.What proportion of black defendants convicted for murdering a white victim were sentenced to death?

f.What proportion of white defendants convicted for murdering a white victim were sentenced to death?

g.Based on the data how many times more likely to be put to death is a black person convicted of killing a white person than a white person convicted of killing a black person?