## Question

1. Imagine that you are in a contest. As your contest entry, choose a whole number between 0 and 100. The winner will be the person whose choice comes closest to two-thirds of the average entry.

2a. Which is the more frequent cause of death in the United States, homicide or stroke? In your answer file, record homicide = 1, stroke = 2.

2b. In respect to homicide and stroke, how much more frequent would you guess is the more frequent of these two causes of death? (For example, if you answered stroke to 2a, and you feel that three times as many people die per year from stroke than homicide, your answer would be 3).

3. Suppose that a university is attempting to predict the grade point average (GPA) of some graduating students based upon their high school GPA levels. In the U.S., a student’s GPA lies in the interval [0, 4]. Below you will find some data, for undergraduates at Santa Clara University, based on students who entered the university in the years 1990, 1991, and 1992. During this period, the mean high school GPA of students who entered as freshmen and subsequently graduated was 3.44 (standard deviation was 0.36). The mean college GPA of those same students was 3.08 (standard deviation 0.40). Suppose that it is your task to predict the graduating college GPA of 3 undergraduate students, based solely on their high school GPA scores. The 3 high school GPAs are 2.2, 3.0, and 3.8. Write down your prediction below for the college GPAs of these students upon graduation.

Prediction of Graduation GPA of student with high school GPA of 2.2 = ______

Prediction of Graduation GPA of student with high school GPA of 3.0 = ______

Prediction of Graduation GPA of student with high school GPA of 3.8 = ______

4. The Dow Jones Industrial Average closed 1999 at 11,497. As a price index, the Dow does not include reinvested dividends. If the Dow were redefined to reflect the reinvestment of all dividends since May 1896, when it commenced at a value of 40, what would its value have been at the end of 1999? In addition to writing down your best guess, also write down a low guess and a high guess so that you feel 90% confident that the true answer will lie between your low guess and your high guess.

Best = ______ Low = ______ High = ______

5. In this question, deducing exact odds from the information provided may require special skills. Most people are unsure about how to solve the problem exactly, so just you do your best.

Imagine 100 book bags, each of which contains 1,000 poker chips. 45 bags contain 700 black chips and 300 red chips. The other 55 bags contain 300 black chips and 700 red chips. You cannot see inside any of the bags. One of the bags is selected at random by means of a coin toss.

Consider the following three questions about the book bag.

5a. What probability would you assign to the event that the selected bag contains predominantly black chips?

Probability = ______________%

5b. Now imagine that 12 chips are drawn, with replacement, from the selected bag. These twelve draws produce 8 blacks and 4 reds. Would you use the new information about the drawing of chips to revise your probability that the selected bag contains predominantly black chips? If so, what new probability would you assign?

Probability = ______________%

5c. In addition to giving your best probability estimate, consider a range: a low estimate and a high estimate so that you feel 90% confident that the right answer will lie between your low estimate and your high estimate. Try not to make the range between your low aestimate and high estimate too narrow. Otherwise, you will appear overconfident. At the same time, try not to make the range between your low estimate and high estimate too wide. This will make you appear underconfident. If you are well-calibrated, you should expect the true probability to lie outside the range between your low estimate and your high estimate one time in ten.

Low estimate = __________% High estimate = ___________%

6. Imagine that there is a bag containing 100 poker chips, 50 black chips and 50 red chips. Suppose that you are offered the choice between accepting a sure $1,000 or playing a 50-50 gamble in which you either win $0 or $2,000. Specifically, you win $2,000 if a black chip is drawn at random from the bag, but $0 if a red chip is drawn. Which would you choose, (1) the sure $1,000; or (2) the gamble?

7. Consider the following variation of the last question. Imagine a bag containing 100 colored chips that are either red or black, but the proportions are unknown to you. Suppose that you are offered the choice between accepting 1) a sure $1,000; 2) a lottery ticket that entitles you to win $2,000 if a red chip is randomly selected from the bag, but $0 otherwise; or 3) a lottery ticket that entitles you to win $2,000 if a black chip is randomly selected from the bag, but $0 otherwise. Which would you choose, 1) the sure $1,000; 2) the lottery ticket where red is the winning color; or 3) the lottery ticket where black is the winning color? Answer 1, 2, or 3.

8. Suppose you face a choice between

A = a guaranteed loss of $745

B = a 25% chance to lose nothing, 75% chance to lose $1000

Which would you choose, the sure loss or the gamble?

9. Sometimes people have to make a series of concurrent choices about sources of risk to which they will be simultaneously exposed. For example, they may use a single insurance agent for their homeowners’ policy, automobile insurance, life insurance, and personal liability coverage. This question simulates exposure to multiple sources of risk. Your first choice is between 9A and 9B, to be followed by a choice between 9C and 9D. Choose between 9A and 9B (circle your choice on the hard copy, use 1 or 0 in the spreadsheet), where:

A = a guaranteed gain of $240

B = 25% chance to win $1000, 75% chance to win nothing

and choose between 9C and 9D (circle your choice on the hard copy, use 1 or 0 in the spreadsheet), where

C = a guaranteed loss of $750

D = 25% chance to lose nothing, 75% chance to lose $1000

10. Imagine that you face the following choice. You can accept a guaranteed $1,500 or play a stylized lottery. The outcome of the stylized lottery is determined by the toss of a fair coin. If heads comes up, you win $1,950. If tails comes up, you win $1,050.

Which would you choose? 1) the guaranteed $1,500 or 2) the lottery?

_________________

11. Imagine that you face the following choice. You can accept a guaranteed loss of $750 or play a stylized lottery. The outcome of the stylized lottery is determined by the toss of a fair coin. If heads comes up, you lose $525. If tails comes up, you lose $975.

Which would you choose? 1) the guaranteed loss of $750 or 2) the lottery?

_________________

12. Imagine that you are in a situation where 75% of the time you lose $760. And 25% of the time you win $240. It’s a risk you have to take. Now I give you a choice.

1. Face the risk I just described and I’ll give you $10,or

2. Face the risk I just described and I’ll give you $0.

Which would you choose, 1 or 2?

13. This question concerns how your attitude to risk depends on other aspects of your financial situation. Imagine that you have just won $1,500 in one stylized lottery, and have the opportunity to participate in a second stylized lottery. The outcome of the second lottery is determined by the toss of a fair coin. If heads comes up, you win $450 in the second lottery. If tails comes up, you lose $450.

Would you choose to participate in the second lottery? Yes (1) or no (2)?

14. Imagine that you have just lost $750 in one stylized lottery, but have the opportunity to participate in a second stylized lottery. The outcome of the second lottery is determined by the toss of a fair coin. If heads comes up, you win $225 in the second lottery. If tails comes up, you lose $225.

Would you choose to participate in the second lottery? Yes (1) or no (2)?

15. Imagine two business people who leave the same hotel at the exact time, to catch different flights at the same airport. By coincidence, their flights are scheduled to depart at the exact same time. Both take taxis and get caught in traffic. They both arrive at the airport at the same time, thirty minutes after the scheduled departure time. Both rush to their gates. Mr. A finds that his flight left at the scheduled time. Ms. B finds that her flight left the gate late, two minutes ago in fact, and is just heading down the runway.

Who feels worse, Mr. A (1) or Ms. B (2)?

Circle your choice.

16. Consider two individuals, Ann and Barbara, who graduated from the same college a year apart. Upon graduation, both took similar jobs with publishing firms. Ann started with a yearly salary of $30,000. During her first year on the job there was no inflation, and in her second year Ann received a 2% ($600) raise in salary. Barbara also started with a yearly salary of $30,000. During her first year on the job there was 4% inflation, and in her second year Barbara received a 5% ($1,500) raise in salary.

16a. As they entered their second year on the job, who was doing better in economic terms? Circle one.

(1) Ann (2) Barbara

16b. As they entered their second year on the job, who do you think was happier? Circle one.

(1) Ann (2) Barbara

16c. As they entered their second year on the job, each received a job offer from another firm. Who do you think was more likely to leave her present position for another job? Circle one.

(1) Ann (2) Barbara

17a. Suppose that you are the only income earner in your family, and you have a good job guaranteed to give you your current (family) income every year for life. You are given the opportunity to take a new and equally good job, with a 50-50 chance it will double your (family) income thereafter and a 50-50 chance that it will cut your (family) income by a third. Would you take the new job? Yes (1) or no (2)? Circle your response below.

YES NO

17b. If you answered NO to question 17a, please skip this question and continue with question 17c. You answered YES to question 17a. Suppose the chances were 50-50 that it would cut it in half. Would you still take the new job? Yes (1) or no (2)? Continue with question 17d.

YES NO

17c. You answered NO to question 6. Suppose the chances were 50-50 that it would double your (family) income and 50-50 that it would cut it by 20%. Would you take the new job? Yes (1) or no (2)?

YES NO

17d. Questions 17a, 17b, and 17c are based on the same data, with one exception: the size of the cut to your (family) income if you take the new job and are unlucky. Having answered these questions, please indicate exactly what the percentage cut x would be that would leave you indifferent between keeping your current job or taking the new job and facing a 50-50 chance of thereafter doubling your income or cutting it by x%.

x = ______%

18. How good a driver are you? Relative to the drivers you encounter on the road, are you (1) above average, (2) average, or (3) below average?

___________________

19. Below you will find a trivia test consisting of ten questions. In addition to giving your best guess, consider a range: a low guess and a high guess so that you feel 90% confident that the right answer will lie between your low guess and your high guess. Try not to make the range between your low guess and high guess too narrow. Otherwise, you will appear overconfident. At the same time, try not to make the range between your low guess and high guess too wide. This will make you appear underconfident. If you are well-calibrated, you should expect that only one out of the ten correct answers does not lie between your low guess and your high guess. (For students who normally use the metric system, note that there are 2.2 pounds in a kilo, 5,280 feet in a mile, and that 1 km corresponds to 5/8 (0.625) of a mile.)

After each question, write down three numbers, your best guess, low guess, and high guess.

19.1 How old was Martin Luther King when he died?

19.2 How long, in miles, is the Nile River?

19.3 How many countries were members of OPEC in 1989?

19.4 According to the conventional canon, how many books are there in the Hebrew Bible?

19.5 What is the diameter, in miles, of the moon?

19.6 What is the weight, in pounds, of an empty Boeing 747?

19.7 In what year was Wolfgang Amadeus Mozart born?

19.8 How long, in days, is the gestation period of an Asian elephant?

19.9 What is the air distance, in miles, from London to Tokyo?

19.10 How deep, in feet, is the deepest known point in the ocean?

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