Questions and Answers of Essentials Of Econometrics

The world’s population was 4.43 billion in 1980 and 6.85 billion in 2010. What was the annual rate of increase during these 30 years? At this rate, what will the world’s population be in the year
The Dow Jones Industrial Average was 240.01 on October 1, 1928 (when the Dow expanded to 30 stocks), and 14,087.55 on October 1, 2007. The CPI was 51.3 in 1928 and 617.7 in 2007. What was the annual
In the 52 years between 1956 and 2008, Warren Buffett’s net worth grew from $100,000 to $62 billion. What was his annual rate of return?
United States real (in 2007 dollars) per capita GDP was $1,504 in 1807 and $45,707 in 2007. What was the annual rate of growth of real per capita GDP over this 200-year period?
The CPI was 51 in 1800 and 25 in 1900. What was the annual percentage rate of change during this 100-year period?
Use the data in Table 3.2 to determine the percentage annual rate of increase in the CPI between 1990 and 2010. 1981 8.9 1996 3.3 1982 3.8 1997 1.7 1983 3.8 1998 1.6 1984 3.9 1999 2.7 1985 3.8 2000
A 1989 radio commercial claimed “If you have a LifeAlert security system, your chances of becoming a victim of a serious crime are 3,000 to 4,000 percent less than your neighbor’s.” Is this
Twelve college women and men were asked to read a short article and, when they were finished, estimate how long it took them to read the article. Table 3.6 shows the actual and estimated times (both
Explain why this statement is incorrect: “When two assets have a +1.00 correlation, they move up and down at the same time, with the same magnitude.”
Calculate the correlation between the official U.S. poverty thresholds for families of four people and the CPI in Table 3.7. Poverty Threshold CPI 1960 $3,022 88.7 1970 $3,968 116.3 1980 $8,414 246.8
After its staff ran more than 5,000 miles in 30 different running shoes, Consumer Reports rated the shoes for overall performance on a scale of 0 to 100. Calculate the correlation between price and
The data in Table 3.9 were used in the 1964 Surgeon General’s Report warning of the health risks associated with smoking, where the first variable is annual per capita cigarette consumption and the
If Y = 10 − 3X, then the correlation between X and Y isa. 1.b. 0.c. −1.d. Undefined. Year Price Index Change from Previous Year Change from 2000 2005 112.2 3.4% 112% 2006 115.9 3.2% 116% 2007
Explain how the following two newspaper headlines that appeared on the same day could both be accurate: “Orders for Machine Tools Increased 45.5% in October” ;“October Orders for Machine Tools
A prominent French mathematician, Jean d’Alembert, argued that because there are four possible outcomes when coins are flipped three times (no heads, a head on the first flip, a head on the second
A very successful football coach once explained why he preferred running the ball to passing it: “When you pass, three things can happen [completion, incompletion, or interception], and two of them
In the game odd-or-even, two players simultaneously reveal a hand showing either one or two fingers. If each player is equally likely to show one or two fingers and their choices are made
A television weather forecaster once said that there was a 50 percent chance of rain on Saturday and a 50 percent chance of rain on Sunday, and therefore a 100 percent chance of rain that weekend.
Jurors are not supposed to discuss a case with anyone until after all of the evidence has been presented. They then retire to the jury room for deliberations, which sometimes begin with a
Suppose that a computer user chooses six random characters (either letters or digits)for a website password. (For example, I just chose ZDQMF2.) Characters can be used more than once (as with ZDZMF2)
What are the chances of winning the following game? Put two red marbles and five blue marbles in a bag. The player puts his hand in the bag and pulls out three marbles.He wins if none of these
The ancient Enneagram (Figure 4.14) has nine personality types represented by the numbers 1 through 9 drawn around a circle. Three equilateral triangles can be drawn by connecting the points 9-3-6,
Answer this letter to newspaper columnist Marilyn vos Savant [17]: “I have a really confusing one for you. Let’s say my friend puts six playing cards face-down on a table. He tells me that
You are playing draw poker and have been dealt a pair of fours, a jack, a seven, and a three. You keep the pair of fours and discard the other three cards. What is the probability that at least one
A police department recorded the clothing colors worn by pedestrians who died after being struck by cars at night [18]. They found that four-fifths were wearing dark clothes and concluded that it is
A book calculated the probabilities of “being injured by various items around your house” and concluded “As the figures show, our homes are veritable booby traps. Even your cocktail table is
A Temple University mathematics professor used these data to show that most Americans have an exaggerated fear of terrorists :Without some feel for probability, car accidents appear to be a
In an interview for a banking job, a student was asked to calculate the following:A can contains 20 coins, 19 of which are ordinary coins and 1 of which has heads on both sides. A coin is randomly
In the United States, criminal defendants are presumed innocent until they are proven guilty beyond a reasonable doubt, because it is thought better to let nine guilty people go free than to send one
Suppose that there are two kinds of households, the Careless and the Careful; 99 percent of households are Careful and 1 percent are Careless. In any given year, a home inhabited by a Careless
Use the information in Exercise 4.17 to answer this question. Suppose that every home is worth $100,000 and that an insurance company sells 1-year policies to every household for $500 that will pay
In three careful studies [21], lie detector experts examined several persons, some known to be truthful and others known to be lying, to see if the experts could tell which were which. Overall, 83
For a woman who gives birth at age 35, the probability of having a baby suffering from Down syndrome is 1/270 [22]. A test of the amniotic fluid in the mother’s uterus is virtually 100 percent
The random walk model of stock prices states that stock market returns are independent of the returns in other periods; for example, whether the stock market does well or poorly in the coming month
The Romeros are planning their family and want an equal number of boys and girls.Mrs. Romero says that their chances are best if they plan to have two children.Mr. Romero says that they have a better
Answer this question that a reader asked Marilyn vos Savant, who is listed in the Guinness Book of World Records Hall of Fame for “Highest IQ” [23]: “During the last year, I’ve gone on a lot
Answer this question that a reader asked Marilyn vos Savant [24]:At a lecture on fire safety that I attended, the speaker said: “One in 10 Americans will experience a destructive fire this year.
An investment advisor claims that 60 percent of the stocks she recommends beat the market. To back up her claim, she recommends n stocks for the coming year. In fact, each of her recommendations has
A woman wrote to Dear Abby, saying that she had been pregnant for 310 days before giving birth [25]. Completed pregnancies are normally distributed with a mean of 266 days and a standard deviation of
A nationwide test has a mean of 75 and a standard deviation of 10. Convert the following raw scores to standardized Z values: X = 94, 83, 75, and 67. What raw score corresponds to a Z value of 1.5?
After Hurricane Katrina, Congress mandated that hurricane protection for New Orleans be improved to a once-in-a-100-years standard, meaning that there is only a 1/100 probability of failing in any
Explaining why he was driving to a judicial conference in South Dakota, the chief justice of the West Virginia State Supreme Court said “I’ve flown a lot in my life.I’ve used my statistical
Yahtzee is a family game played with five normal six-sided dice. In each turn, a player rolls the five dice and can keep some of the numbers and roll the remaining dice. After the second roll, the
At the midpoint of the 1991 Cape Cod League baseball season, Chatham was in first place with a record of 18 wins, ten losses, and one tie [27]. (Ties are possible because games are sometimes stopped
Answer this letter to Ask Marilyn [28]:You’re at a party with 199 other guests when robbers break in and announce that they are going to rob one of you. They put 199 blank pieces of paper in a hat,
Limited Liability is considering insuring Howard Hardsell’s voice for $1,000,000.They figure that there is only a 0.001 probability that they will have to pay off. If they charge $2,000 for this
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
A business is considering building either a one-story or two-story apartment complex.The value of the completed building will depend on the strength of the rental market when construction is
The annual returns on U.S. corporate stock and U.S. Treasury bonds over the next 12 months are uncertain. Suppose that these returns can be described by normal distributions with U.S. corporate stock
In his 1868 work, Carl Wunderlich concluded that temperatures above 100.4°Fahrenheit should be considered feverish. In a 1992 study, Maryland researchers suggested that 99.9° Fahrenheit was a more
The Australian Bureau of Meteorology uses the monthly air-pressure difference between Tahiti and Darwin, Australia, to calculate the Southern Oscillation Index:SOI = 10(X – μ)/σ, where X is the
If the age at death of a 20-year-old U.S. woman is normally distributed with a mean of 76.4 years and a standard deviation of 8.1 years, what is the probability that she will live past 80?
Galileo wrote a short note on the probability of obtaining a sum of 9, 10, 11, or 12 when three dice are rolled [30]. Someone else had concluded that these numbers are equally likely, because there
The noon temperature on July 4 in two cities, A and B, is normally distributed with respective means μA and μB and standard deviations σA and σB. For each of these three cases, identify the city
Mark believes that there is a 4/5 probability that it will snow in Boston on New Year’s Eve 2015; Mindy believes that the probability is only 2/3. What bet could they make that would give each a
Consider a multiple-choice question that has n possible answers. A person who does not answer the question gets a score of 0. A person who answers the question gets +1 if the answer is correct and
On long automobile trips, Mrs. Jones drives and Mr. Jones gives directions. When there is a fork in the road, his directions are right 30 percent of the time and wrong 70 percent of the time. Having
A carnival game has four boxes (Figure 4.15), into which the contestant tosses four balls. Each box is deep enough to hold all four balls and the contestant is allowed to toss each ball until it
Answer this question to Ask Marilyn [31]:I recently returned from a trip to China, where the government is so concerned about population growth that it has instituted strict laws about family size.
A standard die is painted green on four sides and red on two sides and will be rolled six times. You can choose one of these three sequences and will win $25 if the sequence you choose occurs. Which
A car was ticketed in Sweden for parking too long in a limited time zone after a policeman recorded the positions of the two tire air valves on one side of the car (in the one o’clock and eight
Smith will win a prize if he can win two consecutive squash games in a three-game match against Andrabi and Ernst alternately, either Andrabi-Ernst-Andrabi or Ernst-Andrabi-Ernst. Assume that Andrabi
Here is a probability variant of a three-card Monte game used by street hustlers. You are shown three cards: one black on both sides, one white on both sides, and one white on one side and black on
What data might be used to make a reasonable estimate of the probability that a 65-year-old man dies within the next 5 years?
What data might be used to make a reasonable estimate of the probability that a newborn baby will be female?
Explain how you would obtain a simple random sample from this population: varsity athletes at your school.
Explain how you would obtain a simple random sample from this population: stocks traded on the New York Stock Exchange (NYSE).
Identify an appropriate population for each of these samples:a. The price of Cheerios in ten stores is recorded.b. Ten Toyota Camrys are driven 1,000 miles and the miles per gallon are recorded.c.
Identify an appropriate population for each of these samples:a. A coin is flipped 100 times and lands heads 54 times.b. A baseball player gets 86 base hits in 300 times at bat.c. Two thousand people
In the 1920s, a vaccine called BCG was tested to see if it could reduce deaths from tuberculosis [11]. A group of doctors gave the vaccine to children from some tubercular families and not to others,
Shere Hite sent detailed questionnaires (which, according to Hite, took an average of 4.4 hours to fill out) to 100,000 women and received 4,500 replies, 98 percent saying that they were unhappy in
A study of the effects of youth soccer programs on self-esteem found that children who played competitive soccer had more self-esteem than other children. Identify the most important statistical bias
A study found that, among youths between the ages of 8 and 18 who were playing competitive soccer, those who had been playing for several years liked soccer more than did those who had been playing
A study looked at a random sample of 100 companies whose stocks were traded on the NYSE. The companies were divided into quintiles (the 20 largest companies, the 20 next largest, and so on) and the
A study of the 30 largest U.S. companies found that their average growth rate over the preceding 20 years had been well above the average growth rate for all companies, suggesting that big companies
A study of the geographic mobility looked at how often adult daughters moved outside the ZIP code in which they were born [14]. The study found that the daughters of immigrants to the United States
The daughters of women who immigrate to the United States have more upward economic mobility than the daughters of women born in the United States, suggesting that U.S. women have less economic
Average grades are higher in senior-level college chemistry courses than in introductory chemistry courses, suggesting that students who get bad grades in an introductory chemistry course should not
In 1993, a member of a presidential task force on food assistance stated “If you think that blacks as a group are undernourished, look around at the black athletes on television—they’re a
The data in Table 5.3 show the fraction of all divorces based on the month in which the marriage ceremony was performed [16]. For example, 6.4 percent of all divorces involve couples who were married
A doctor notices that more than half of her teenage patients are male, while more than half of her elderly patients are female. Does this mean that males are less healthy than females when young, but
Explain any possible flaws in this conclusion [17]:A drinker consumes more than twice as much beer if it comes in a pitcher than in a glass or bottle, and banning pitchers in bars could make a dent
Red Lion Hotels ran full-page advertisements claiming “For every 50 business travelers who try Red Lion, a certain number don’t come back. But 49 of 50 do.” The basis for this claim was a
A medical insurance survey found that more than 90 percent of the plan’s members are satisfied. Identify two kinds of survivor bias that may affect these results. Is the reported satisfaction rate
A survey found that the average employee at the WD Company had worked for the company for 20 years, suggesting that the average person who takes a job with WD works for the company for 20 years.
A study of students at a very selective liberal arts college found that varsity athletes had, on average, higher grades than nonathletes. The researcher concluded that the college could increase the
A New York Times article argued that one reason many students do not graduate from college within 6 years of enrolling is that they choose to “not attend the best college they could have” [18].
A major California newspaper [19] asked its readers the following question: “Do you think the English-only law should be enforced in California?” Of the 2,674 persons who mailed in responses, 94
A doctor told a meeting of the Pediatric Academic Societies that a U.S. government survey of 4,600 high school students found that both boys and girls were much more likely to have smoked cigarettes,
Explain why these data are not convincing evidence that the way to seize more illegal drugs is to conduct fewer searches: “In 2000, [the U.S. Customs service] conducted 61 percent fewer searches
Reuters Health [22] reported that In a study of more than 2,100 secondary school students, researchers found that boys who used computers to do homework, surf the Internet and communicate with others
A study of college seniors found that economics majors had above-average scores on a test of mathematical ability, suggesting that the study of economics improves mathematical ability. Identify the
A study of college graduates found that economics majors had higher average starting salaries than art history majors, suggesting that the study of economics increases your chances of getting a good
A study found that college students who take more than one course from a professor give the professor higher course evaluations than do students who take only one course from the professor,
A study found that professors tend to give higher grades to students who take more than one course from the professor than to students who take only one course from the professor, suggesting that
A Volvo advertisement said that the average American drives for 50 years and buys a new car, on average, every 3¼ years—a total of 15.4 cars in 50 years. Since Volvos last an average of 11 years
A study looked at the 50 states in the United States and compared educational spending per student in each state with the average score on college entrance examination tests (the SAT and ACT). There
Studies have shown that people who marry and divorce have, on average, fewer children than do people who stay married, suggesting that having more children makes divorce less likely.a. Explain why
Studies have shown that students who go to highly selective colleges have, on average, higher lifetime incomes than do students who go to less selective colleges.a. Explain why there might be
A 1950s study found that married men were in better health than men of the same age who never married or were divorced, suggesting that the healthiest path is for a man to marry and never divorce

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