ECO 380 – Quantitative Critical Thinking Wesley Pech
Second Exam
December 5, 2016
(10 points)1. Two coins are selected, and each one is tossed 21 times. The two sequences of Heads and Tails were:
Coin A: TTHTTTTHHTHTHHHHHHTHT
Coin B: HTTTHHTHTHTHTHHTHTTHT
Given this information, answer the following questions:
a)If it is known that these two coins are unbiased, which sequence is more likely to happen? Explain.
b)If we know that only one of these two coins is biased, and we have to guess which one, what is our best guess? Explain.
(10 points)2. The policy of one school was to punish students for being late, while the corresponding policy in an otherwise identical school was to reward students for being on time. If effectiveness is measured by behavior on the day following punishment or reward, which policy would seem to be more effective? Is this standard of effectiveness a good one?
(10 points)3. Germany is the most populous country in Europe. Suppose the following rankings are constructed for European countries: meat consumption per capita, cancer death rates, and height. What is your best guess for where Germany will be placed in these rankings? Explain.
(25 points)4. The graph below shows happiness at time t on the horizontal axis and happiness at time t+1 on the vertical axis. The solid line is the 45-degree line. Based on this information, answer the following questions:
a)Why is the 45-degree line a good reference point to use?
b)Draw this graph on your blue book and add a scatter plot that shows a positive correlation between the two variables, but that also shows regression to the mean.
c)Draw this graph again, and add a scatter plot that shows a positive correlation between the two variables, but that shows regression away from the mean. Why is this scatter plot unrealistic?
(15 points)5. It is well known that chess players have on average higher levels of IQ than non-chess players. Why can’t we jump to the conclusion that the practice of chess causes intelligence?
(15 points)6. Many people say “Every time I chose X I felt better afterwards.” Name the reasons why we should still be skeptical about the causal effect of X on this person’s well-being.
(15 points)7. Suppose a research study investigated the correlation between years of schooling and average salary, and found a positive correlation between the two variables. But the authors divided the data by gender, and found that among males, the correlation between these two variables is 0.4, whereas for females it is 0.7.
a)What does this mean?
b)Show why we can’t conclude that schooling has more impact on the average salary of females than on the salary of males.