Econ 57 Fall 2002 Midterm

1. For each of the following studies, identify the type of graph (histogram, side-by-side boxplots, scatter diagram, or time series graph) that would be the the MOST appropriate:

a. Has air pollution in Claremont generally risen or fallen during the past 20 years?

b. Do colleges that accept a large percentage of their students in early-decision programs have higher yields (percentage of accepted students that enroll)?

c. Can college grade point averages be predicted from high school grade point averages?

d. Students who get more sleep get higher grades.e. Is there more dispersion in the starting salaries of economics majors or English majors?

2. The NCAA championship basketball tournament involves 63 games. In 2001 Sandbox.com offered \$10 million to anyone who could correctly predict the winners of all 63 games before the tournament began. (In 2002, the company offered a variety of prizes plus a promise that the company’s president would eat a bucket of worms if anyone correctly predicted all 63 winners.) If you have a 70% chance of correctly predicting the winner of each game, what is the probability that you will correctly predict the winners of all 63 games?

3. A carnival game has three boxes, into which the contestant tosses three balls:

Each box is deep enough to hold all three balls and the contestant is allowed to toss each ball until it lands in a box. The contestant wins the prize if each box has one ball. Assuming that balls are equally likely to land in any box (this is a game of chance, not skill), what is the probability of winning the game?

4. Each student who is admitted to a certain college has a 0.6 probability of attending that college and a 0.4 probability of going somewhere else. Each student’s decision is independent of the decisions of other students. Compare a college that admits 1000 students with a larger college that admits 2500 students. Which college has the higher probability that the percentage of the students admitted who decide to attend the college will be

a. exactly equal to 60%?

b. between 50% and 70%?

c. more than 80%?

5. Explain why these data are not convincing evidence that distributing daily planners to college students would reduce alcohol consumption, recreational drug use, and smoking:

Don’t put off for tomorrow what you can accomplish today. A recent study by two professors at Carleton University in Ottawa, Canada, shows that college students who don’t heed this age-old saying about procrastination are more likely to engage in unhealthy behaviors [alcohol consumption, recreational drug use, and smoking]. [“Health affected by Procrastination,” The Student Life, September 27, 2002.]

6. A survey of the prices of houses recently sold in Claremont obtained the data below. Display these data in a histogram.

 sale price (\$) number of houses 100,000 - 200,000 10 200,000 - 500,000 60 500,000 - 1,000,000 30

7. Two baseball teams will play 5 games against each other. In each game, Team A has a 0.6 probability of winning and Team B has a 0.4 probability of winning. What is the probability that Team B will win at least 3 of these 5 games?

8. Suppose that all houses are worth \$200,000 and that there are two kinds of households, the Careless and the Careful; 90 percent of households are Careful and 10 percent are Careless. There is a 0.010 probability that fire will destroy a home inhabited by Careless people, but only a 0.001 probability that fire will destroy a Careful home. If a fire destroys a home, what is the probability that it was a home occupied by careless people?

9. Use the data given in the preceding exercise to evaluate a fire insurance policy that costs \$1,000 and will pay \$200,000 if a home is destroyed by fire and \$0 otherwise.

a. Has the insurance company priced the policy correctly in the sense that, if everyone buys insurance, the expected value of the payoff is less than the \$1,000 cost?

b. From the standpoint of a Careful household, what is the expected value of the payoff?

c. From the standpoint of a Careless household, what is the expected value of the payoff?