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descriptive statistics
Seeing Through Statistics 3rd Edition David D Busch, Jessica M Utts - Solutions
8. In financial situations, are businesses or individuals more likely to make use of expected value for making decisions? Explain.
7. The U.C. Berkeley Wellness Encyclopedia (1991) contains the following statement in its discussion of HIV testing: “In a high-risk population, virtually all people who test positive will truly be infected, but among people at low risk the false positives will outnumber the true positives. Thus,
*6. Find a dollar bill or other item with a serial number. Write down the number.I predict that there is something unusual about it or some pattern to it. Explain what is unusual about it and how I was able to make that prediction.
5. Why is it not surprising that the night before a major airplane crash several people will have dreams about an airplane disaster? If you were one of those people, would you think that something amazing had occurred?
4. Suppose two sisters are reunited after not seeing each other since they were 3 years old. They are amazed to find out that they are both married to men named James and that they each have a daughter named Jennifer. Explain why this is not so amazing.
3. Explain why it is not at all unlikely that in a class of 50 students two of them will have the same last name.
*2. Give an example of a sequence of events to which the gambler’s fallacy would not apply because the events are not independent.
1. Although it’s not quite true, suppose the probability of having a male child(M) is equal to the probability of having a female child (F). A couple has four children.a. Are they more likely to have FFFF or to have MFFM? Explain your answer.b. Which sequence in part a of this exercise would a
4. Estimate the probability of some event in your life using a personal probability, such as the probability that a person who passes you on the street will be wearing a hat. Use an event for which you can keep a record of the relative frequency of occurrence over the next week. How well calibrated
3. Find a journal article that describes an experiment designed to test the kinds of biases described in this chapter. Summarize the article, and discuss what conclusions can be made from the research. You can find such articles by searching appropriate bibliographic databases and trying key words
2. Find and explain an example of a marketing strategy that uses one of the techniques in this chapter to try to increase the chances that someone will purchase something. Do not use an exact example from the chapter, such as “buy one, get one free.”
1. Design and conduct an experiment to try to elicit misjudgments based on one of the phenomena described in this chapter. Explain exactly what you did and your results.
18. Guess at the probability that if you ask five people when their birthdays are, you will find someone born in the same month as you. For simplicity, assume that the probability that a randomly selected person will have the same birth month you have is 112. Now use the material from Chapter 16
17. Suppose you have a friend who is willing to ask her friends a few questions and then, based on their answers, is willing to assess the probability that those friends will get an A in each of their classes. She always assesses the probability to be either .10 or .90. She has made hundreds of
*16. Explain which of the concepts in this chapter might contribute to the decision to buy a lottery ticket.
15. Give one example of how each of the following concepts has had or might have an unwanted effect on a decision or action in your daily life:a. Conservatismb. Optimismc. Forgotten base ratesd. Availability
*14. Suppose you go to your doctor for a routine examination, without any complaints of problems. A blood test reveals that you have tested positive for a certain disease. Based on the ideas in this chapter, what should you ask your doctor in order to assess how worried you should be?
13. Explain how the concepts in this chapter account for each of the following scenarios:a. Most people rate death by shark attacks to be much more likely than death by falling airplane parts, yet the chances of dying from the latter are actually 30 times greater (Plous, 1993, p. 121).b. You are a
12. Barnett (1990) examined front page stories in the New York Times for 1 year, beginning with October 1, 1988, and found 4 stories related to automobile deaths but 51 related to deaths from flying on a commercial jet. These correspond to 0.08 story per thousand U.S. deaths by automobile and 138.2
11. In the early 1990’s, there were approximately 5 billion people in the world.Plous (1993, p. 5) asked readers to estimate how wide a cube-shaped tank would have to be to hold all of the human blood in the world. The correct answer is about 870 feet, but most people give much higher answers.
10. Explain how an insurance salesperson might try to use each of the following concepts to sell you insurance:a. Anchoringb. Pseudocertaintyc. Availability
*9. Determine which statement (A or B) has a higher probability of being true and explain your answer. Using the material in this chapter, also explain which statement you think a statistically naive person would think had a higher probability.A. A car traveling 120 miles per hour on a two-lane
8. Research by Slovic and colleagues (1982) found that people judged that accidents and diseases cause about the same number of deaths in the United States, whereas in truth diseases cause about 16 times as many deaths as accidents. Using the material from this chapter, explain why the researchers
7. In this chapter, we learned that one way to lower personal-probability assessments that are too high is to list reasons why you might be wrong. Explain how the availability heuristic might account for this phenomenon.
6. A telephone solicitor recently contacted the author to ask for money for a charity in which typical contributions are in the range of $25 to $50. The solicitor said, “We are asking for as much as you can give, up to $300.00.” Do you think the amount people give would be different if the
*5. Explain why you should be cautious when someone tries to convince you of something by presenting a detailed scenario. Give an example.
4. Suppose a defense attorney is trying to convince the jury that his client’s wallet, found at the scene of the crime, was actually planted there by his client’s gardener.Here are two possible ways he might present this to the jury:Statement A: The gardener dropped the wallet when no one was
3. There are many more termites in the world than there are mosquitoes, but most of the termites live in tropical forests. Using the ideas in this chapter, explain why most people would think there were more mosquitoes in the world than termites.
*2. Suppose a television advertisement were to show viewers a product and then say, “You might expect to pay $25, $30, or even more for this product. But we are offering it for only $16.99.” Explain which of the ideas in this chapter is being used to try to exploit viewers.
1. Explain how the pseudocertainty effect differs from the certainty effect.
4. Find two lottery or casino games that have fixed payoffs and for which the probabilities of each payoff are available. (Some lottery tickets list them on the back of the ticket or on the lottery’s Web site. Some books about gambling give the payoffs and probabilities for various casino
3. Pick an event that will result in the same outcome for everyone, such as whether it will rain next Saturday. Ask 10 people to assess the probability of that event, and note the variability in their responses. (Don’t let them hear each other’s answers, and make sure you don’t pick something
2. Flip a coin 100 times. Stop each time you have done 10 flips (that is, stop after 10 flips, 20 flips, 30 flips, and so on), and compute the proportion of heads using all of the flips up to that point. Plot that proportion versus the number of flips. Comment on how the plot relates to the
1. Refer to Exercise 12. Present the question to 10 people, and note the proportion who answer with alternative B. Explain to the participants why it cannot be the right answer, and report on their reactions.
28. On November 9, 2001 the Sacramento Bee reported, “Using new data, scientists have dramatically lowered the odds [that an asteroid will wipe out the Earth].They now say there’s just a 1-in-5,000 chance that an asteroid bigger than halfa-mile wide will hit the Earth in the next 100 years”
27. Find out your yearly car insurance cost. If you don’t have a car, find out the yearly cost for a friend or relative. Now assume you will either have an accident or not, and if you do, it will cost the insurance company $5000 more than the premium you pay. Calculate what yearly accident
*26. We have seen many examples for which the term expected value seems to be a misnomer. Construct an example of a situation where the term expected value would not seem to be a misnomer for what it represents.
25. In 1991, 72% of children in the United States were living with both parents, 22% were living with mother only, 3% were living with father only, and 3%were not living with either parent (World Almanac and Book of Facts, 1993, p. 945). What is the expected value for the number of parents a
*24. Suppose the probability that you get an A in any class you take is .3 and the probability that you get a B is .7. To construct a grade-point average, an A is worth 4.0 and a B is worth 3.0. What is the expected value for your grade-point average? Would you expect to have this grade-point
23. In the “3 Spot” version of the former California Keno lottery game, the player picked three numbers from 1 to 40. Ten possible winning numbers were then randomly selected. It cost $1 to play. The table shows the possible outcomes.Compute the expected value for this game. Interpret what it
22. Remember that the probability that a birth results in a boy is about .51. You offer a bet to an unsuspecting friend. Each day you will call the local hospital and find out how many boys and how many girls were born the previous day. For each girl, you will give your friend $1 and for each boy
21. Suppose you have to cross a train track on your commute. The probability that you will have to wait for a train is 15, or .20. If you don’t have to wait, the commute takes 15 minutes, but if you have to wait, it takes 20 minutes.a. What is the expected value of the time it takes you to
20. According to Krantz (1992, p. 161), the probability of being injured by lightning in any given year is 1685,000. Assume that the probability remains the same from year to year and that avoiding a strike in one year doesn’t change your probability in the next year.a. What is the probability
19. Lyme disease is a disease carried by ticks, which can be transmitted to humans by tick bites. Suppose the probability of contracting the disease is 1100 for each tick bite.a. What is the probability that you will not get the disease when bitten once?b. What is the probability that you will not
18. Suppose you routinely check coin-return slots in vending machines to see if they have any money in them. You have found that about 10% of the time you find money.a. What is the probability that you do not find money the next time you check?b. What is the probability that the next time you will
*17. Read the definition of “independent events” given in Rule 3. Explain whether each of the following pairs of events is likely to be independent:*a. A married couple goes to the voting booth. Event A is that the husband votes for the Republican candidate; event B is that the wife votes for
16. Use your own particular expertise to assign a personal probability to something, such as the probability that a certain sports team will win next week. Now assign a personal probability to another related event. Explain how you determined each probability, and explain how your assignments are
15. People are surprised to find that it is not all that uncommon for two people in a group of 20 to 30 people to have the same birthday. We will learn how to find that probability in a later chapter. For now, consider the probability of finding two people who have birthdays in the same month. Make
*14. In Section 16.2, you learned two ways in which relative-frequency probabilities can be determined. Explain which method you think was used to determine each of the following probabilities:*a. The probability that a particular flight from New York to San Francisco will be on time is .78.b. On
13. Example 3 in this chapter states that “the probability that a piece of checked luggage will be temporarily lost on a flight with a U.S. airline is 1176.” Interpret that statement, using the appropriate interpretation of probability.
12. A study by Kahneman and Tversky (1982, p. 496) asked people the following question: “Linda is 31 years old, single, outspoken, and very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in
11. The probability that a randomly selected American adult belongs to the American Automobile Association (AAA) is .10 (10%), and the probability that that person belongs to the American Association of Retired Persons (AARP) is .11(11%) (Krantz, 1992, p. 175). What assumption would we have to make
10. Suppose the probability that you get an interesting piece of mail on any given weekday is 110. Is the probability that you get at least one interesting piece of mail during the week (Monday to Friday) equal to 510? Why or why not?
*9. A small business performs a service and then bills its customers. From past experience, 90% of the customers pay their bills within a week.*a. What is the probability that a randomly selected customer will not pay within a week?*b. The business has billed two customers this week. What is the
8. Suppose you wanted to determine the probability that someone randomly selected from the phone book in your town or city has the same first name as you.a. Assuming you had the time and energy to do it, how would you go about determining that probability? (Assume all names listed are spelled
7. Suppose you wanted to test your ESP using an ordinary deck of 52 cards, which has 26 red and 26 black cards. You have a friend shuffle the deck and draw cards at random, replacing the card and reshuffling after each guess. You attempt to guess the color of each card.a. What is the probability
*6. Explain why probabilities cannot always be interpreted using the relativefrequency interpretation. Give an example of where that interpretation would not apply.
5. Explain which of the following more closely describes what it means to say that the probability of a tossed coin landing with heads up is 12:Explanation 1: After more and more tosses, the fraction of heads will get closer and closer to 12.Explanation 2: The number of heads will always be about
4. According to Krantz (1992, p. 111), the probability of being born on a Friday the 13th is about 1214.a. What is the probability of not being born on a Friday the 13th?b. In any particular year, Friday the 13th can occur once, twice, or three times.Is the probability of being born on Friday the
3. There is something wrong in each of the following statements. Explain what is wrong.a. The probability a randomly selected driver will be wearing a seat belt is .75, whereas the probability that he or she will not be wearing one is .30.b. The probability that a randomly selected car is red is
*2. Use the probability rules in this chapter to solve each of the following:*a. The probability that a randomly selected Caucasian American child will have blonde or red hair is 23%. The probability of having blonde hair is 14%.What is the probability of having red hair?b. According to Blackenhorn
1. Recall that there are two interpretations of probability: relative frequency and personal probability.a. Which interpretation applies to this statement: “The probability that I will get the flu this winter is 30%”? Explain.b. Which interpretation applies to this statement: “The probability
5. How much would you be willing to pay for a ticket to a contest in which there was a 1% chance that you would win $500 and a 99% chance that you would win nothing?Explain your answer.
4. Why do you think insurance companies charge young men more than they do older men for automobile insurance, but charge older men more for life insurance?
3. Explain what’s wrong with the following statement, given by a student as a partial answer to Thought Question 1b: “The probability that I will eventually own a home, or of any other particular event happening, is 12 because either it will happen or it won’t.”
2. Explain what it means for someone to say that the probability of his or her eventually owning a home is 70%.
1. Here are two very different queries about probability:a. If you flip a coin and do it fairly, what is the probability that it will land heads up?b. What is the probability that you will eventually own a home; that is, how likely do you think it is? (If you already own a home, what is the
3. In addition to the Dow Jones Industrial Average, there are other indicators of fluctuation in stock prices. Two examples are the New York Stock Exchange Composite Index and the Standard and Poor’s 500. Choose a stock index (other than the Dow Jones) and write a report about it. Include whether
2. Find an example of a time series plot presented in a newspaper, magazine, journal, or Web site. Discuss the plot based on the information given in this chapter.Comment on what you can learn from the plot.
1. Plot your own resting pulse rate taken at regular intervals for 5 days. Comment on which of the components of time series are present in your plot. Discuss what you have learned about your own pulse from this exercise.
18. According to the World Almanac and Book of Facts (1995, p. 380), the population of Austin, Texas (reported in thousands), has grown as follows:Year 1950 1960 1970 1980 1990 Population 132.5 186.5 253.5 345.5 465.6a. Of the three nonrandom components of time series (trends, seasonal, and
17. Explain why it is important to examine a time series for many years before making conclusions about the contribution of each of the three nonrandom components.
16. The Dow Jones Industrial Average reached a high of $7801.63 on December 29, 1997. Recall from Section 15.4 that it reached a high of $842.00 on December 29, 1970. The Consumer Price Index averaged 38.8 for 1970; for 1997, it averaged 160.5. By what percentage did the high in the DJIA increase
*15. The CPI in July 1977 was 60.9; in July 1994, it was 148.4.*a. The salary of the governor of California in July 1977 was $49,100; in July 1994, it was $120,000. Compute what the July 1977 salary would be in July 1994, adjusted for inflation, and compare it with the actual salary in July
14. Suppose you have been hired as a salesperson, selling computers and software.In January, after 6 months on the job, your sales suddenly plummet. They had been high from August to December. Your boss, who is also new to the position, chastises you for this drop. What would you say to your boss
13. Explain why it is important for economic time series to be seasonally adjusted before they are reported.
12. Draw an example of a time series that hasa. Trend, cycles, and random fluctuations, but not seasonal components.b. Seasonal components and random fluctuations, but not trend or cycles.
11. Which of the three nonrandom components of time series (trend, seasonal, or cycles) is likely to contribute the most to the unadjusted Consumer Price Index?Explain.
*10. Discuss which of the three components of a time series (trend, seasonal, and cycles)are likely to be present in each of the following series, reported monthly for the past 10 years:*a. Unemployment rates*b. Hours per day the average child spends watching television*c. Interest rates paid on a
9. Explain which one of the components of an economic time series would be most likely to be influenced by a major war. (See Section 15.2.)
*8. Suppose a time series across 60 months has a long-term positive trend. Would you expect to find a correlation between the values in the series and the months 1 to 60? If so, can you tell from the information given whether it would be positive or negative?
7. Many statistics related to births, deaths, divorces, and so on across time are reported as rates per 100,000 of population rather than as actual numbers. Explain why those rates may be more meaningful as a measure of change across time than the actual numbers of those events.
6. The population of the United States rose from about 179 million people in 1960 to about 281 million people in 2000. Suppose you wanted to examine a time series to see if homicides had become an increasing problem over that time period.Would you simply plot the number of homicides versus time, or
5. If you wanted to present a time series of the yearly cost of tuition at your local college for the past 30 years, adjusted for inflation, how would you do the adjustment?
*4. If you were to present a time series of the yearly cost of tuition at your local college for the past 30 years, would it be better to first adjust the costs for inflation?Explain.
3. Global warming is a major concern because it implies that temperatures around the world are going up on a permanent basis. Suppose you were to examine a plot of monthly temperatures in one location for the past 50 years. Explain the role that the three time series components (trend, seasonal,
2. For each of the time series in Exercise 1, explain whether there is likely to be a seasonal component.
*1. For each of the following time series, do you think the long-term trend would be positive, negative, or nonexistent?*a. The cost of a loaf of bread measured monthly from 1960 to 2004.*b. The temperature in Boston measured at noon on the first day of each month from 1960 to 2004.c. The price of
2. Find a news article that reports on current values for one of the indexes discussed in this chapter. Discuss the news report in the context of what you have learned in this chapter. For example, does the report contain any information that might be misleading to an uneducated reader? Does it
1. Numerous economic indicators are compiled and reported by the U.S. government and by private companies. Various sources are available at the library and on the Internet to explain these indicators. Write a report on one of the following.Explain how it is calculated, what its uses are, and what
21. In 1950, being a millionaire was touted as a goal that would be achievable by very few people. The CPI in 1950 was 24.1, and in 2002 it was 179.9. How much money would one need to have in 2002 to be the equivalent of a millionaire in 1950, adjusted for inflation? Does it still seem like a goal
20. The United States Census Bureau, Statistical Abstract of the United States 1999, p. 877, contains a table listing median family income for each year from 1947 to 1997. The incomes are presented “in current dollars” and “in constant (1997)dollars.” As an example, the median income in
19. Refer to the previous exercise. Find out the current minimum wage and the current Consumer Price Index. (These were available as of November 2003 at the Web sites http://www.dol.gov/esa/minwage/chart.htm and http://www.bls.gov/cpi/, respectively.) Determine what the minimum wage should be at
18. An article in the Sacramento Bee (Stafford, 2003) on July 7, 2003 reported that the current minimum wage is only $5.15 an hour and that it has not kept pace with inflation. The Consumer Price Index at the time (the end of June 2003) was 183.7.a. One of the quotes in the article was “to keep
*17. Two of the economic indicators measured by the U.S. government are “Number of employees on nonagricultural payrolls” and “Average duration of unemployment, in weeks.” One of these is designated as a “lagging economic indicator”and the other is a “coincident economic indicator.”
16. Examine the 11 series that make up the Index of Leading Economic Indicators, listed in Table 14.2. Choose at least two of the series to support the explanation given by the government in March 1994 that the drop in these indicators in February was partially due to severe winter weather.
15. One of the components of the Index of Leading Economic Indicators is the Index of Consumer Expectations. Why do you think this index would be a leading economic indicator?
14. Many U.S. government payments, such as social security benefits, are increased each year by the percentage change in the CPI. In 1995, the government started discussions about lowering these increases or changing the way the CPI is calculated.According to an article in the New York Times,
13. The Bureau of Labor Statistics reports that one use of the Consumer Price Index is to periodically adjust the federal income tax structure, which sets higher tax rates for higher income brackets. According to the BLS, “these adjustments prevent inflation-induced increases in tax rates, an
*12. Most newspaper accounts of the Consumer Price Index report the percentage change in the CPI from the previous month rather than the value of the CPI itself.Why do you think that is the case?
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