Econ 57
Economic Statistics
Spring 2006
HW 2 assignment
1. Are stocks or bonds a better investment? Using ibbotson3.xls, compare stocks and bonds by
analyzing their summary statistics (mean, median, standard deviation). And then compare stocks
and bonds by graphing the box plots of their returns. How do these two approaches to analyzing
the data complement one another? What is the difference between the box plot of returns and the
histogram of returns?
2. Based on the box plots below, what can you determine about the relationship between selfrating of attractiveness and happiness? (Hint: By “relationship,” I mean the relationship between
attractiveness self-rating score and happiness for each person).
3. Are blacks stopped by police more often than whites? Create a visual display comparing the
probability of being stopped if white vs the probability of being stopped if black using the data in
driving.xls. Write a two sentence summary of your findings based on this data.
4. When data were grouped into 16 age categories, female death rates were higher in Costa Rica
than in Sweden in every single age group; yet the overall female death rate was lower in Costa
Rica than in Sweden (8.12 vs 9.29 per 1000 women). How can you explain this phenomenon?
5. On September 2, 1998, the New York Times reported evidence of high school grade inflation.
They showed that a greater proportion of high school students were getting top grades while at
the same time SAT Math scores had declined for every grade category by about 2-4 points over
the decade. Explain how everyone’s scores can go down while the average goes up. Show this
phenomenon by giving a numerical example by filling in MATH scores in the shaded cells of the
table below.
Grade in
1988
1998
1988 Mean
1998 Mean
school
(%)
(%)
Math Score
Math Score
A+
4%
7%
632
629
A
11%
15%
A13%
16%
B
53%
48%
C
19%
14%
Total
100%
100%
Wtd Average: 504
6. Assume that tests for AIDS are 98% accurate. If you have AIDS, then the test is positive 98%
of the time. If you don’t have AIDS, the test is negative 98% of the time. Assume that 0.5% of the
population has AIDS (1/200).
a) What is the probability of having AIDS if you test +? Does this result warrant worrying?
b) What is the probability of not having AIDS if you test positive?
c) What is the probability of not having AIDS if you test negative?
d) What is the probability of having AIDS if you test negative?
e) How accurate would you say the testing procedure is, on scale of 1-10 (10 is most
accurate)? Justify your answer.
f) If the test for AIDS were 99.5% accurate for both positive and negative readings, what
would be the probability of having AIDS if you test positive (assuming .005 of the
population has AIDS)? Compare your answer to (a) above and explain why you get this
result.
g) What would happen to the probability of having AIDS if you test positive assuming that
2% of the population has AIDS (and assuming a 98% accuracy rate)? Compare your
answer to (a) above and explain why you get this result.
h) What would happen to the probability of having AIDS if you test positive assuming 2%
of the population has AIDS and the accuracy rate of the test goes up to 99.5% for both
positive and negative readings? Compare your answer to (a) above.
k) What is the probability of having AIDS if you test positive twice in a row? Compare
your answer to (a) above and explain why the probability goes up.
7. From this article below, is the probability of accident given silver car necessarily low if the
probability of silver car given accident low? Explain the difference. Explain what is misleading in
this article. (Hint: Set up a contingency table with Accident and No Accident on the top and
Silver and other colors on the left side. Then assume that P(S|A) < .5P(Non Silver|A), that there
are 1071 total cars, and that there are 500 accidents and 571 non-accidents. The fraction P(S|No
Accident) and P(other color| No Accident) can vary. But notice what is implied or not implied if
the fraction of P(S|No Accident) is less than half of all the non-accidents. What do you take away
as a larger conclusion from the exercise?)
Silver Colored Cars Safest, New Zealand Scientists Say
(Reuters Dec 19, 2003)
LONDON (Reuters) - Silver colored cars are less likely to be involved in a crash causing
serious injuries, New Zealand scientists said Friday.
About 3,000 people die in road traffic accidents around the world each day but researchers at
the University of Auckland said the risk of being injured in a silver car was less than in cars of
other colors.
"Silver cars were about 50 percent less likely to be involved in a crash resulting in serious injury
than white cars," Sue Furness and her colleagues said in a report in The British Medical Journal.
The researchers studied the impact of car color on the risk of a serious injury in a study of more
than 1,000 drivers in New Zealand between 1998 and 1999.
About half the drivers had been involved in a crash in which one or more occupants had been
admitted to hospital or died while 571 had not had crashes and acted as a control group.
After taking into account factors such as the age and sex of the driver, the use of seat belts, the
age of the vehicle and the road conditions, color still had an impact.
The researchers said there was an increased risk of a serious injury in brown cars and the odds
were also higher for black and green cars.
They did not explain why car color has an influence but said previous research suggested that
white or light-colored cars are less likely to be involved in a crash than cars of other colors.
"Increasing the proportion of silver cars could be an effective passive strategy to reduce the
burden of injury from car crashes," Furness added.