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descriptive statistics
Seeing Through Statistics 3rd Edition David D Busch, Jessica M Utts - Solutions
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 September 2003 was 185.2. Following are the values for some of the subcategories, taken from the CPI Web site:Dairy products 170.3 Fruits, vegetables 222.4 Alcoholic beverages 187.9 Rent 206.6
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 an
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 14.3, explain why it may not do so accurately.
4. When the CPI was computed for December 2002, the relative weight for the food and beverages category was 15.6%, whereas for the recreation category it was only 5.9%. 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 2000 were Year 1940 1950 1960 1970 1980 1990 2000 CPI 14.0 24.1 29.6 38.8 82.4 130.7 172.2*a. 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
1. The price of a first-class stamp in 1970 was 8 cents, whereas in 2002 it was 37 cents. The Consumer Price Index for 1970 was 38.8, whereas for 2002 it was 172.2. If the true cost of a first-class stamp did not increase between 1970 and 2002, what should it have cost in 2002? In other words, what
3. Find a journal article that uses a chi-square test.a. State the hypotheses being tested.b. Write the contingency table.c. Give the value of the chi-square statistic and the p-value as reported in the article.d. Write a paragraph or more (as needed) explaining what was tested and what was
2. Find a poll that has been conducted at two different time periods or by two different sources. For instance, many polling organizations ask opinions about certain issues on an annual or other regular basis.a. Create a 2 2 table where “time period” is one categorical variable and
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
*24. The table at the top of the next page shows participants categorized by sex and by whether they were observed conversing (yes, no).a. State the null and alternative hypotheses that can be tested with this table.*b. What is the expected count for “Male, Yes?” Find the remaining expected
23. The accompanying figure provides Minitab computer output for testing for a relationship between sex and “External distraction” but the expected counts have been removed for you to fill in.a. Fill in the expected counts.b. State the null and alternative hypotheses being tested.c. Give the
22. Refer to Table 8 on page 37 of Original Source 5 on the CD. Notice that there is a footnote to the table that reads “*p.05 and **p.01, based on chi-square test of association with sex.” The footnote applies to “Grooming**” and “External distraction*.”a. Explain what null and
*21. Participants were asked how many times in the past year they had experienced at least one of the 13 hangover symptoms listed. Responses were categorized as 0 times, 1–2 times, 3–11 times, 12–51 times, and 52 times. For the purposes of this exercise, responses have been categorized as
20. One of the statements in the Original Source was “men and women were equally likely to experience at least one of the hangover symptoms in the past year(men: 89%; women: 87%; chi-square statistic 1.2, p 0.282)” (Slutske, Piasecki, and Hunt-Carter, 2003, p. 1445).a. State the null and
*19. One of the results in the Original Source was “there were only two symptoms that men experienced more often than women: vomiting (men: 50%; women:44%; chi-square statistic 4.7, p 0.031) and sweating more than usual (men:34%; women: 23%; chi-square statistic 18.9, p 0.001)”
18. What population do you think is represented by the sample for this study?Explain.
17. This is a continuation of Exercise 17 in Chapter 12. Kohler (1994, p. 427) reported 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. The
16. This is a continuation of Exercise 16 in Chapter 12. The data (shown in the accompanying table) are reproduced from Case Study 12.1 and represent employees laid off by the U.S. Department of Labor.Ethnic Group Laid Off Not Laid Off Total African American 130 1382 1512 White 87 2813 2900 Total
*15. 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
14. This is a continuation of Exercise 15 in Chapter 12. A case-control study in Berlin, reported by Kohlmeier et al. (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
13. In Exercise 9 of Chapter 12 results were given for a Roper Poll in which people were classified according to age and were asked if they had ever seen a ghost.The results from asking Minitab to compute the chi-square statistic are shown in Figure 13.4. What can you conclude about the
12. Refer to Example 1, investigating the relationship between taking aspirin and risk of heart attack. As shown in Table 12.1 on page 219, 104 of the 11,037 aspirin takers had heart attacks, whereas 189 of the 11,034 placebo takers had them. Carry out the chi-square test for this study. (The
*11. A political poll based on a random sample of 1000 likely voters classified them by sex and asked them if they planned to vote for Candidate A or Candidate B in the upcoming election. Results are shown in the accompanying table.*a. State the null and alternative hypotheses in this situation.b.
10. Refer to the previous exercise. In each case, state the null and alternative hypotheses.
9. In each of the following situations, specify the population. Also, state the two categorical variables that would be measured for each unit in the sample and the two categories for each variable.a. Researchers want to know if there is a relationship between having graduated from college or not
*8. For each of the following chi-square statistics or p-values based on a chi-square test for a 2 2 table, would the relationship be statistically significant?*a. chi-square statistic 1.42b. chi-square statistic 4.5*c. p-value 0.01d. p-value 0.15
7. For each of the following possible conclusions, state whether it would follow when the p-value is greater than 0.05:a. Reject the null hypothesis.b. Reject the alternative hypothesis.c. Accept the null hypothesis.d. Accept the alternative hypothesis.e. The relationship is not statistically
6. For each of the following possible conclusions, state whether it would follow when the p-value is less than 0.05:a. Reject the null hypothesis.b. Reject the alternative hypothesis.c. Accept the null hypothesis.d. Accept the alternative hypothesis.e. The relationship is not statistically
*5. Explain what “expected counts” represent. In other words, under what condition are they “expected”?
4. Are null and alternative hypotheses statements about samples, about populations, or does it depend on the situation? Explain.
3. Suppose a relationship between two variables is found to be statistically significant.Explain whether each of the following is true in that case:a. There is definitely a relationship between the two variables in the sample.b. There is definitely a relationship between the two variables in the
*2. If there is no relationship between two variables in a population, which is more likely to result in a statistically significant relationship in a sample—a small sample, a large sample, or are they equivalent? Explain. (Hint: If there is no relationship in the population, how often will the
1. If there is a relationship between two variables in a population, which is more likely to result in a statistically significant relationship in a sample from that population—a small sample, a large sample, or are they equivalent? Explain.
3. Refer to News Story 12, “Working nights may increase breast cancer risk” in the Appendix and on the CD and the accompanying three journal articles on the CD.Write a two- to four-page report describing how the studies were done and what they found in terms of relative risks and odds ratios.
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 5 in each cell and be sure the individuals you use
22. Refer to Original Source 10, “Religious attendance and cause of death over 31 years” on the CD. For this study, the researchers used a complicated statistical method to assess relative risk by adjusting for factors such as education and income.The resulting numbers are called “relative
*21. Refer to the Additional News Source accompanying News Story 10 on the CD,“‘Keeping the faith’ UC Berkeley researchers links weekly church attendance to longer, healthier life.” Based on the information in the story, identify or calculate a numerical value for each of the following:*a.
20. Refer to News Story 10 in the Appendix and on the CD, “Churchgoers live longer, study finds.” One of the statements in the news story is “women who attend religious services regularly are about 80 percent as likely to die as those not regularly attending.” Discuss the extent to which
*19. Read News Story 13 in the Appendix and on the CD, “3 factors key for drug use in kids.” Identify the statistical term for the number(s) in bold in each of the following quotes (for example, relative risk).*a. “And kids with $25 or more a week in spending money are nearly twice as likely
18. Read News Story 13 in the Appendix and on the CD, “3 factors key for drug use in kids.” Identify or calculate a numerical value for each of the following from the information in the news story:a. The increased risk of smoking, drinking, getting drunk, or using illegal drugs for teens who
*17. 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
16. The data in Table 12.12 are reproduced from Case Study 12.1 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
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 ac- tual breakdown of data for specific programs is confidential,
*13. Reporting on a study of drinking and drug use among college students in the United States, a Newsweek reporter wrote:Why should college students be so impervious to the lesson of the morning after? Efforts to discourage them from using drugs actually did work. The proportion of college
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
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. In a test for extrasensory perception (ESP), described in Case Study 13.1 in the next chapter, people were asked to try to use psychic abilities to describe a hidden photo or video segment being viewed by a “sender.” They were then shown four choices and asked which one they thought was the
*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
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
25. The following are titles of some of the news stories in the Appendix. In each case, determine whether the study was a randomized experiment or an observational study, then discuss whether the title is justified based on the way the study was done.a. News Story 3: “Rigorous veggie diet found
24. News Story 20: “Eating Organic Foods Reduces Pesticide Concentrations in Children.”
23. News Story 16: “More on TV Violence.”
*22. News Story 15: “Kids’ stress, snacking linked.”
21. News Story 12: “Working nights may increase breast cancer risk.”
20. News Story 10: “Churchgoers live longer, study finds.”
19. An article in The Wichita Eagle (24 June 2003, p. 4A) read as follows:Scientists have analyzed autopsy brain tissue from members of a religious order who had an average of 18 years of formal education and found that the more years of schooling, the less likely they were to exhibit Alzheimer’s
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 (1 June 1996, 149, 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 article
*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 or an electronic journal resource 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
1. (Computer or statistics calculator required.) Measure the heights and weights of 10 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 or calculator that produces regression equations, find the regression
17. Refer to the journal article given as Original Source 2 on the CD, “Development and initial validation of the Hangover Symptoms Scale: Prevalence and correlates of hangover symptoms in college students.” On page 1447 it says: “The HSS [Hangover Symptoms Scale] was significantly positively
*16. In 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 distance
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 2010 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 2002. A regression equation relating winning time and year for 1924 to 1998 is winning time 264.5 (0.1142)(year)*a.
*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 actual*a. Predict the ideal weight for a man who weighs 150 pounds and for a woman who
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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