Exam One
Econ 180: Quantitative Methods
Professor Robert J. Lemke
Spring 2006

Directions: A bluebook has been provided for your answers. In order to facilitate anonymous grading, put your ID number (not your name) on your bluebook. There are five questions to the exam, each worth equal weight.

1. Consider a sample of data: S = {4, 6, 7, 4, 5, 3, 2, 6, 11, 8, 10}.

   1. What is the sample mean?

   2. What is the sample variance?

   3. What is the coefficient of variation?

   4. What is the z-score associated with the sample value of 8?

   5. What is the second element of the ordered sample?
   
   
   

2. Let X be a discrete random variable with the following probability distribution function:
   
   

   x			1			2			3			4			5
   p(x)			0.40			0.30			0.15			0.10			0.05

   1. What is the probability that X takes a value above 3?

   2. What is the probability that X takes a value of at most 2?

   3. What is the probability that X takes a value of 5?

   4. What is the mean of X?

   5. What is the variance of X?
   
   
   

3. At a particular college, it is known that 70 percent of students receive financial aid, while 30 percent do not receive financial aid. A random sample of 8 students is obtained.

   1. What is the probability that exactly 7 of the students receive financial aid?

   2. What is the probability that at least 6 of the students receive financial aid?
   
   
   
   

4. In a random sample of 200 households, it is determined that 80 households have at least one person living in it with a college degree (so that 120 households have no college degree). It is also determined that 150 households give charitable contributions on a regular basis (so that 50 do not give to charity on a regular basis). Finally, it is known that education (i.e., having a college degree) and charitable giving are independent traits across households.

   1. How many of the 200 households do not have a college degree and give to charity on a regular basis?

   2. How many of the 80 college-educated households give to charity on a regular basis?
   
   
   

5. The Career Development Center of an elite liberal arts college surveyed its 347 graduating seniors concerning their GPA and the number of job offers they received. The CDC created the following cross-tabulation of the data:
   
   

   						Number of Job Offers
   						0			1			2			3			4
   GPA			3.50 - 4.00			2			8			26			34			3
   			3.00 - 3.49			9			25			78			62			8
   			2.00 - 2.99			10			29			13			4			1
   			0.00 - 1.99			13			14			8			0			0

   1. How many students graduated with at least a 2.00 grade point average?

   2. The CDC analyzes the data and concludes the over-riding theme is that students with higher grade point averages tend to receive more job offers. A student with a 1.5 grade point average looks at the table and responds that the CDC is wrong because 29 students with a GPA between 2.00 and 2.99 received one job offer while only 25 students with a GPA between 3.00 and 3.49 and only 8 students with a GPA between 3.5 and 4.0 received one job offer. How would you respond to this analysis?

   3. What is the probability of receiving 2 or more job offers if one's GPA is at least 3.5?

   4. For each GPA class, what is the probability of receiving at least one job offer?

   5. What is the expected number of job offers for a student whose GPA is between 3.00 and 3.49? What is the expected number of job offers for a student whose GPA is between 2.00 and 2.99?