SCCC 312A – ProSeminar in Statistics

Lecture Homework #6

Due Date: 2/16/04 (2/18/04)

Attention: First Exam will be this Friday, February 20, 1:25-2:15PM.

Coverage: All topics including those in this problem set.

There is a practice test in the Exam Info Folder of the course website.

Part I: Book Problems

On pages 178-179 do: 4.51, 4.54, 4.57

On pages 185-187 do: 4.62, 4.63, 4.66, 4.67, 4.70, 4.72, 4.76

On pages 191-192 do: 4.81, 4.84

Additional Problem

Assume that the percentage of students at USC who are Republicans is 45%, and the other 55% are either Democrats or Independents. Among Republicans, 70% will respond “Yes” to the following question: “Is George W. Bush doing an acceptable job as President?”; whereas among non-Republicans, 35% will respond “Yes” to the same question.

Suppose that one USC student is randomly chosen, and is asked the question: “Is George W. Bush doing an acceptable job as President?” Let

A = event that the student is a Republican;

B = event that the student responds “Yes” to the question.

Answer the following questions:

1. What is the probability of A, P(A)? what is P(A^c)?

2. What is the probability of B given A?

3. What is the probability of B given A^c?

4. What is the probability of B?

5. Given the information that the student responded “Yes” to the question, what is the probability that he/she is a Republican? Compare this probability with that in A.

6. Given the information that the student responded “No” to the question, what is the probability that he/she is not a Republican?