Q1)A research study estimated that under a certain condition, the probability a

subject would be referred for heart catheterization was 0.906 for whites and

0.847 for blacks.

a. A press release about the study stated that the odds of referral for cardiac

catheterization for blacks are 60% of the odds for whites. Explain how they

obtained 60% (more accurately, 57%).

b. An Associated Press story that described the study stated "Doctors were only

60% as likely to order cardiac catheterization for blacks as for whites."

Q2)Data posted at the FBI website (www.fbi.gov) stated that of all blacks slain in

2005, 91% were slain by blacks, and of all whites slain in 2005, 83% were

slain by whites. Let Y denote race of victim and X denote race of murderer.

a. Which conditional distribution do these statistics refer to, Y given X, or X

given Y ?

b. Calculate and interpret the odds ratio between X and Y .

c. Given that a murderer was white, can you estimate the probability that the

victim was white? What additional information would you need to do this?

(Hint: How could you use Bayes's Theorem?)

Q3)A 20-year study of British male physicians (R. Doll and R. Peto, British Med. J.,

2: 1525-1536, 1976) noted that the proportion who died from lung cancer was

0.00140 per year for cigarette smokers and 0.00010 per year for nonsmokers.

The proportion who died from heart disease was 0.00669 for smokers and

0.00413 for nonsmokers.

a. Describe the association of smoking with lung cancer and with heart disease,

using the difference of proportions, the relative risk, and the odds ratio.

Interpret.

b. Which response (lung cancer or heart disease) is more strongly related to

cigarette smoking, in terms of the reduction in deaths that could occur with

an absence of smoking?