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Seeing Through Statistics 2nd Edition Jessica M. Utts - Solutions

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 1/2:Explanation 1: After more and more tosses, the fraction of heads will get closer and closer to 1/2.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 1/214.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
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 website. 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 14.4 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 1994.b.
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 has:a. Trend, cycles, and random fluctuations, but not seasonal componentsb. 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 ratesb. Hours per day the average child spends watching televisionc. 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 14.2.)
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 249 million people in 1990. 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,
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 1998b. The temperature in Boston measured at noon on the first day of each month from 1960 to 1998c. The price of a
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
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 13.2. 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?
11. As mentioned in this chapter, both the base year and the relative weights used for the Consumer Price Index are periodically updated.a. Why is it important to update the relative weights used for the CPI?b. Explain why the base year is periodically updated.
10. In addition to the overall CPI, the BLS reports the index for the subcategories.The overall CPI in 1993 was 144.5. Following are the values for some of the subcategories, taken from the World Almanac and Book of Facts (1995, p. 110):Dairy products 129.4 Fruits, vegetables 159.0 Alcoholic
9. Find out what the tuition and fees were for your school for the previous 4 years and the current year. Using the cost 5 years ago as the base, create a “tuition index” for each year since then. Write a short summary of your results that would be understood by someone who does not know what
8. In explaining why it is a costly mistake to have the CPI overestimate inflation, the Associated Press (20 October 1994) reported, “Every 1 percentage point increase in the CPI raises the federal budget deficit by an estimated $6.5 billion.”Explain why that would happen.
7. Suppose that you gave your niece a check for $50 on her 16th birthday in 1997(when the CPI was 160.5). Your nephew is now about to turn 16. You discover that the CPI is now 180. How much should you give your nephew if you want to give him the same amount you gave your niece, adjusted for
6. Americans spent the following amounts for medical care between 1987 and 1993, in billions of dollars (World Almanac and Book of Facts, 1995, p. 128).Year 1987 1988 1989 1990 1991 1992 1993 Amount Spent 399.0 487.7 536.4 597.8 651.7 704.6 760.5a. Create a “medical care index” for each of
5. Remember that the CPI is supposed to measure the change in what it costs to maintain the same standard of living that was in effect during the base year(s).Using the material in Section 13.3, explain why it may not do so accurately.
4. When the CPI was computed for December 1997, the relative weight for the food and beverages category was 16.3%, whereas for the recreation category it was only 6.1%. Explain why food and beverages received higher weight than recreation.
3. A paperback novel cost $1.50 in 1968, $3.50 in 1981, and $6.99 in 1995. Compute a “paperback novel price index” for 1981 and 1995 using 1968 as the base year. In words that can be understood by someone with no training in statistics, explain what the resulting numbers mean.
2. The CPIs at the start of each decade from 1940 to 1990 were Year 1940 1950 1960 1970 1980 1990 CPI 14.0 24.1 29.6 38.8 82.4 130.7a. Determine the percentage increase in the CPI for each decade.b. During which decade was inflation the highest, as measured by the percentage change in the CPI?c.
1. The price of a first-class stamp in 1970 was 8 cents, whereas in 1997 it was 32 cents. The Consumer Price Index for 1970 was 38.8, whereas for 1997 it was 160.5. If the true cost of a first-class stamp did not increase between 1970 and 1997, what should it have cost in 1997? In other words, what
2. Find a news story that discusses a study showing increased (or decreased) risk of one variable based on another. Write a report evaluating the information given in the article and discussing what conclusions you would reach based on the information in the article. Discuss whether any of the
1. Carefully collect data cross-classified by two categorical variables for which you are interested in determining whether there is a relationship. Do not get the data from a book or journal; collect it yourself. Be sure to get counts of at least five in each cell and be sure the individuals you
20. The chi-squared statistic for the data in Exercise 19 is about 220, so the differences observed in the approval rates are clearly statistically significant. Now suppose that a random sample of 890 applicants had been examined, a sample size 100 times smaller than the one reported. Further,
19. Kohler (1994, p. 427) reports data on the approval rates and ethnicity for mortgage applicants in Los Angeles in 1990. Of the 4096 African American applicants, 3117 were approved. Of the 84,947 white applicants, 71,950 were approved.a. Construct a contingency table for the data.b. Compute the
18. The data in Table 12.16 are reproduced from Case Study 12.2 and represent employees laid off by the U.S. Department of Labor.a. Compute the odds of being retained to being laid off for each ethnic group.b. Use your results in part a to compute the odds ratio and confirm that it is about 3.0, as
17. Howell (1992, p. 153) reports on a study by Latané and Dabbs (1975) in which a researcher entered an elevator and dropped a handful of pencils, with the appearance that it was an accident. The question was whether the males or females who observed this mishap would be more likely to help pick
16. Compute the chi-squared statistic and assess the statistical significance for the relationship between bird ownership and lung cancer, based on the data in Exercise 15.
15. A case-control study in Berlin, reported by Kohlmeier, Arminger, Bartolomeycik, Bellach, Rehm, and Thamm (1992) and by Hand et al. (1994), asked 239 lung cancer patients and 429 controls (matched to the cases by age and sex)whether they had kept a pet bird during adulthood. Of the 239 lung
14. A well-known example of Simpson’s Paradox, published by Bickel, Hammel, and O’Connell (1975), examined admission rates for men and women who had applied to graduate programs at the University of California at Berkeley. The actual breakdown of data for specific programs is confidential, but
13. Reporting on a study of drinking and drug use among college students in the United States, a Newsweek reporter wrote:a. What was the relative risk of cocaine use for college students in 1980 compared with college students in 1993? Write your answer as a statement that could be understood by
12. According to Consumer Reports (1995 January, p. 29), “Among nonsmokers who are exposed to their spouses’ smoke, the chance of death from heart disease increases by about 30%.” Rewrite this statement in terms of relative risk, using language that would be understood by someone who does not
11. A statement quoted in this chapter was, “Clinically depressed people are at a 50 percent greater risk of killing themselves” (Newsweek, 18 April 1994, p. 48).This means that when comparing people who are clinically depressed to those who are not, the former have an increased risk of killing
10. Using the terminology of this chapter, what name (for example, odds, risk, relative risk) applies to each of the boldface numbers in the following quotes?a. “Fontham found increased risks of lung cancer with increasing exposure to secondhand smoke, whether it took place at home, at work, or
9. The Roper Organization (1992) conducted a study as part of a larger survey to ascertain the number of American adults who had experienced phenomena such as seeing a ghost, “feeling as if you left your body,” and seeing a UFO. A representative sample of adults (18 and over) in the continental
8. A newspaper story released by the Associated Press noted that “a study by the Bureau of Justice Statistics shows that a motorist has about the same chance of being a carjacking victim as being killed in a traffic accident, 1 in 5000” [Davis(CA) Enterprise, 3 April 1994, p. A9]. Discuss this
7. Refer to the ESP experiments described in Case Study 12.1. By chance alone, 25% of the guesses would be expected to be successful. In the experiment, 34%of the guesses were successful. In both parts a andb, express your answer in a full sentence.a. What are the odds of a successful guess by
6. The headline in an article in the Sacramento Bee read “Firing someone? Risk of heart attack doubles”(Haney, 1998). The article explained that “Between 1989 and 1994, doctors interviewed 791 working people who had just undergone heart attacks about what they had done recently. The
5. Raloff (1995) reported on a study conducted by Dimitrios Trichopolous of the Harvard School of Public Health in which researchers “compared the diets of 820 Greek women with breast cancer and 1548 others admitted to Athens-area hospitals for reasons other than cancer.” One of the results had
4. Science News (25 February 1995, p. 124) reported a study of 232 people, aged 55 or over, who had heart surgery. The patients were asked whether their religious beliefs give them feelings of strength and comfort and whether they regularly participate in social activities. Of those who said yes to
3. According to the University of California at Berkeley Wellness Letter (February 1994, p. 1), only 40% of all surgical operations require an overnight stay at a hospital. Rewrite this fact as a proportion, as a risk, and as the odds of an overnight stay. In each case, express the result as a full
2. According to the World Almanac and Book of Facts (1995, p. 964), the rate of deaths by drowning in the United States in 1993 was 1.6 per 100,000 population.Express this statistic as a percentage of the population; then explain why it is better expressed as a rate than as a percentage.
1. Suppose a study on the relationship between gender and political party included 200 men and 200 women and found 180 Democrats and 220 Republicans. Is that information sufficient for you to construct a contingency table for the study? If so, construct the table. If not, explain why not.
2. Peruse journal articles and find two examples of scatterplots for which the authors have computed a correlation that you think is misleading. For each case, explain why you think it is misleading.
1. Find a newspaper or journal article that describes an observational study in which the author’s actual goal is to try to establish a causal connection. Read the article, and then discuss how well the author has made a case for a causal connection. Consider the factors discussed in Section 11.4
18. In Case Study 10.1, we learned how psychologists relied on twins to measure the contributions of heredity to various traits. Suppose a study were to find that identical (monozygotic) twins had highly correlated scores on a certain trait but that pairs of adult friends did not. Why would that
17. Lave (1990) discussed studies that had been done to test the usefulness of seat belts before and after their use became mandatory. One possible method of testing the usefulness of mandatory seat belt laws is to measure the number of fatalities in a particular region for the year before and the
16. An article in the Davis (CA) Enterprise (5 April, 1994) had the headline,“Study: Fathers key to child’s success.” The article described a new study as follows: “The research, published in the March issue of the Journal of Family Psychology, found that mothers still do a disproportionate
15. Construct an example for which correlation between two variables is masked by grouping over a third variable.
14. It is said that a higher proportion of drivers of red cars are given tickets for traffic violations than the drivers of any other color car. Does this mean that if you drove a red car rather than a white car, you would be more likely to receive a ticket for a traffic violation? Explain.
13. Explain why it would probably be misleading to use correlation to express the relationship between number of acres burned and number of deaths for major fires in the United States.
12. Suppose a positive relationship had been found between each of the following sets of variables. In Section 11.3, seven potential reasons for such relationships are given. Explain which of the seven reasons is most likely to account for the relationship in each case. If you think more than one
11. According to The Wellness Encyclopedia (University of California, 1991, p.17): “Alcohol consumed to excess increases the risk of cancer of the mouth, pharynx, esophagus, and larynx. These risks increase dramatically when alcohol is used in conjunction with tobacco.” It is obviously not
10. Construct an example of a situation where an outlier deflates the correlation between two variables. Draw a scatterplot.
9. Construct an example of a situation where an outlier inflates the correlation between two variables. Draw a scatterplot.
8. Suppose a study measured total beer sales and number of highway deaths for 1 month in various cities. Explain why it would make sense to divide both variables by the population of the city before determining whether a relationship exists between them.
7. Refer to Case Study 10.2, in which students reported their ideal and actual weights. When males and females are not separated, the regression equation is ideal = 8.0 + 0.9 actuala. Draw the line for this equation and the line for the equation ideal = actual on the same graph. Comment on the
6. Which one of the seven reasons for relationships listed in Section 11.3 is supposed to be ruled out by designed experiments?
5. Give an example of two variables that are likely to be correlated because they are both changing over time.
4. Iman (1994, p. 505) presents data on how college students and experts perceive risks for 30 activities or technologies. Each group ranked the 30 activities. The rankings for the eight greatest risks, as perceived by the experts, are shown in Table 11.5.a. Prepare a scatterplot of the data, with
3. An article in Science News (vol. 149, 1 June, 1996, p. 345) claimed that “evidence suggests that regular consumption of milk may reduce a person’s risk of stroke, the third leading cause of death in the United States.” The claim was based on an observational study of 3150 men, and the
2. Suppose a study of employees at a large company found a negative correlation between weight and distance walked on an average day. In other words, people who walked more weighed less. Would you conclude that walking causes lower weight? Can you think of another potential explanation?
1. Explain why a strong correlation would be found between weekly sales of firewood and weekly sales of cough drops over a 1-year period. Would it imply that fires cause coughs?
2. Go to your library and peruse journal articles, looking for examples of scatterplots accompanied by correlations. Find three examples in different journal articles.Present the scatterplots and correlations, and explain in words what you would conclude about the relationship between the two
1. (Computer required.) Measure the heights and weights of ten friends of the same sex. Draw a scatterplot of the data, with weight on the vertical axis and height on the horizontal axis. Using a computer that produces regression equations, find the regression equation for your data. Draw it on
16. As one of the examples in this chapter, we noticed a very strong relationship between husbands’ and wives’ ages for a sample of 200 British couples, with a correlation of .94. Coincidentally, the relationship between putting distance and success rate for professional golfers had a
15. The original data for the putting success of professional golfers included values beyond those we used for this example (5 feet to 15 feet), in both directions. At a distance of 2 feet, 93.3% of the putts were successful. At a distance of 20 feet, 15.8% of the putts were successful.a. Use the
14. The regression equation relating distance (in feet) and success rate (percent) for professional golfers, based on 11 distances ranging from 5 feet to 15 feet, is success rate = 76.5 – (3.95)(distance)a. What percent success would you expect for these professional golfers if the putting
13. Explain why we should not use the regression equation we found in Exercise 12 for speed-skating time versus year to predict the winning time for the 2002 Winter Olympics.
12. In Chapter 9, we examined a picture of winning time in men’s 500-meter speed skating plotted across time. The data represented in the plot started in 1924 and went through 1992. The regression equation relating winning time and year is winning time = 255 – (0.1094)(year)a. Would the
11. Refer to Case Study 10.2, in which regression equations are given for males and females relating ideal weight to actual weight. The equations are Women: ideal = 43.9 + 0.6 actual Men: ideal = 52.5 + 0.7 actuala. Predict the ideal weight for a man who weighs 150 pounds and for a woman who weighs
10. The regression line relating verbal SAT scores and GPA for the data exhibited in Figure 9.5 is GPA = 0.539 + (0.00362)(verbal SAT)a. Predict the average GPA for those with verbal SAT scores of 500.b. Explain what the slope of 0.00362 represents.c. The lowest possible SAT score is 200. Does the

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