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mathematics
statistics
Seeing Through Statistics 4th Edition Jessica M.Utts - Solutions
Table 9.3 indicates the population (in millions) and the number of violent crimes (in millions) in the United States from 1982 to 1991, as reported in the World Almanac and Book of Facts (1993, p. 948). (Thankfully, both numbers and rates of violent crime started dropping in 1992 and have continued
Collect some categorical data on a topic of interest to you, and represent it in a statistical picture. Explain what you have done to make sure the picture is as useful as possible.
Collect two measurement variables on each of at least 10 individuals. Represent them in a statistical picture. Describe the picture in terms of possible outliers, variability, and relationship between the two variables.
Find some data that represent change over time for a topic of interest to you. Present a line graph of the data in the best possible format. Explain what you have done to make sure the picture is as useful as possible.
For each of the following pairs of variables measured for cities in North America, explain whether the relationship between them would be a deterministic one or a statistical one. a. Geographic latitude of the city and average temperature in January for the city. b. Average temperature in January
Give an example of a pair of variables that are likely to have a positive correlation and a pair of variables that are likely to have a negative correlation.
Explain how two variables can have a perfect curved relationship and yet have zero correlation. Draw a picture of a set of data meeting those criteria.
The table below gives the average June and December temperatures (in Fahrenheit) for eight cities in the United States. City June December Anchorage 55.0 18.6 Bismarck 64.7 16.2 Boston 67.7 34.7 Chicago 68.9 27.7 Dallas 81.3 47.1 New York 70.4 37.7 Phoenix 90.5 56.1 Portland 63.6 40.4a. Draw a
Refer to the previous exercise, giving the regression equation relating verbal SAT and GPA. a. Explain what the slope of 0.00362 represents. b. The lowest possible SAT score is 200. Does the intercept of 0.539 have any useful meaning for this example? Explain.
Refer to the equation for women in the previous exercise, relating ideal and actual weight. a. Does the intercept of 43.9 have a logical physical interpretation in the context of this example? Explain. b. Does the slope of 0.6 have a logical interpretation in the context of this example? Explain.
Outliers in scatterplots may be within the range of values for each variable individually but lie outside the general pattern when the variables are examined in combination. A few points in Figures 10.9 and 10.10 could be considered as outliers. In the context of this example, explain the
In Chapter 9, we examined a picture of winning time in men’s 500meter speed skating plotted across time. The data represented in the plot started in 1924 and went through 2010. A regression equation relating winning time and year for 1924 to 2006 is winning time 5 273.06 2 (0.11865)( year) a.
For each of the following pairs of variables measured on college students, explain whether the relationship between them would be a deterministic one or a statistical one. a. Hours per day spent studying, on average, and hours per night spent sleeping, on average. b. Height in inches and height in
The original data for the putting success of professional golfers included values beyond those we used in Exercise 22 (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
Refer to the temperature data given in the table accompanying Exercise 12. a. Using Excel, a calculator, or other software, find the intercept and slope for the regression equation with x = average June temperature and y = average December temperature for these cities. b. Use the equation you found
The table below gives the self-reported heights of 10 college women (“Daughter’s height”), along with the heights of their mothers. Daughter’s height (y) Mother’s height
Refer to the previous exercise about the relationship between mothers’ and daughters’ heights. Would the intercept of the regression line relating x = Mother’s height to y = Daughter’s height have a useful interpretation in this situation? (You do not need to compute the regression line to
Refer to the temperature data given in Exercise 12. A regression equation could be computed to relate x = average June temperature and y = average December temperature across cities. (This was requested in Exercise 25.) Answer the following questions without actually computing the regression
Refer to the journal article given as Original Source 2 on the companion website, “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
A pint of water weighs 1.04 pounds, so 1 pound of water is 0.96 pint. Suppose a merchant sells water in containers weighing 0.5 pound, but customers can fill them to their liking. It is easier to weigh the filled container than to measure the volume of water the customer is purchasing. Define x to
Are each of the following pairs of variables likely to have a positive correlation or a negative correlation? a. Daily temperatures at noon in New York City and in Boston measured for a year. b. Weights of automobiles and their gas mileage in average miles per gallon. c. Hours of television watched
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 equation for your data. Draw it on your scatter
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
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.
Construct an example of a situation in which an outlier inflates the correlation between two variables. Draw a scatterplot.
Construct an example of a situation in which an outlier deflates the correlation between two variables. Draw a scatterplot.
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
a. Number of deaths from automobiles and beer sales for each year from 1950 to 1990. b. Number of ski accidents and average wait time for the ski lift for each day during one winter at a ski resort.
a. Stomach cancer and consumption of barbecued foods, which are known to contain carcinogenic (cancercausing) substances. b. Self reported level of stress and blood pressure.
a. Amount of dietary fat consumed and heart disease. b. Twice as many cases of leukemia in a new high school built near a power plant than at the old high school.
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.
Construct an example for which correlation between two variables is masked by grouping over a third variable.
Each of the following headlines reported on an observational study. In each case, explain whether or not you think the headline is warranted. If not, write a more suitable headline. a. “Morning people are happier than night owls, study suggests.”
An article in the Davis (CA) Enterprise (April 1994) had the headline “Study: Fathers key to child’s success.” The article described the study as follows: “The research, published in the March issue of the Journal of Family Psychology, found that mothers still do a disproportionate share
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 year
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
One of the features that may suggest a cause-and-effect relationship from an observational study is a “dose-response” relationship. a. Explain what is meant by a dose-response relationship. b. Give an example of a possible dose-response relationship. c. Can a dose-response relationship exist if
News Story 8: “Education, kids strengthen marriage.”
News Story 12: “Working nights may increase breast cancer risk.”
News Story 16: “More on TV Violence.”
News Story 20: “Eating Organic Foods Reduces Pesticide Concentrations in Children.” Exercises 30 and 31 list the titles of some of the news stories printed or summarized in the Appendix. In each case, determine whether the study was a randomized experiment or an observational study, then
a. News Story 2: “Research shows women harder hit by hangovers.” b. News Story 15: “Kids’ stress, snacking linked. c. News Story 20: “Eating Organic Foods Reduces Pesticide Concentrations in Children.”
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 noted
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
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 58.0 10.9 actual a. Draw the line for this equation and the line for the equation ideal 5 actual on the same graph. Comment on the graph
Find a news story 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,
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
(Computer software required.) Find two variables that are both changing over time. A good source is government data available at the website fedstats.gov.Record the values of the two variables for at least eight time periods (such as years).a. Create a scatterplot of the data, and comment on the
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
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
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
Refer to the previous exercise and Table 12.10. a. What is the relative risk of reportedly seeing a ghost for one group compared to the other? Write your answer in the form of a sentence that could be understood by someone who knows nothing about statistics. b. Repeat part (a) using increased risk
Drug use among college students in the United States was particularly heavy during the 1970s. Reporting on a study of drinking and drug use among college students in the United States in 1994, a Newsweek reporter wrote: Why should college students be so impervious to the lesson of the morning
Refer to the quote in the previous exercise, about marijuana and cocaine use in 1980 and 1993. 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 someone who does not know
In a survey for a statistics class project, students in the class were asked whether they commute to school by car (Yes or No) and whether they had ever received a parking ticket (Yes or No). Of the 23 students who com-muted to school by car, 19 had received a parking ticket. Of the 25 students who
A case-control study in Berlin, reported by Kohlmeier, Arminger, Bartolomeycik, Bellach, Rehm, and Thamm (1992) and by Hand and colleagues (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
In Example 12.4 and Table 12.5, we presented data from Australia showing that the likelihood of couples separating depended on whether the wife’s parents had been divorced. For this exercise, we consider the likelihood of the couple separating based on whether the husband’s parents had been
Refer to Exercise 21 and Table 12.11, investigating the risk of separation for Australian couples based on whether the husband’s parents had been divorced. a. What are the odds of a couple separating to not separating when the husband’s parents had been divorced? b. What are the odds of a
A statement quoted in this chapter was, “Use of aspirin for five years or longer was tied to a 30-percent reduction in skin cancer risk [for women aged 50 to 79], according to findings published in the journal Cancer” (Pittman, 14 March 2013). a. What term from this chapter applies to the
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
One of your teachers tells your class that skip-ping class often can lead to dire consequences. He says that data from his previous classes show that students who often skip class have twice the risk of failing compared to students who attend regularly, even though class attendance and
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
A well-known example of Simpson’s Paradox, published by Bickel, Hammel, and O’Connell (1975), and 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
In a survey for a statistics class project, students in the class were asked if they had ever been in a traffic accident, including a minor “fender-bender.” Of the 23 males in the class, 16 reported having been in an accident. Of the 34 females in the class, 18 reported having been in an
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 are frequently bored, compared with those who are not. b. The relative risk of smoking, drinking,
a. The relative risk of dying from circulatory diseases for people who attended religious services less than once a week or never, compared to those who attended at least weekly. b. The increased risk of dying from digestive diseases for people who attended religious services less than once a week
News Story 10, described in the Appendix, is titled “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 each of
The relative risk of dying from all causes for women under age 70, for those who do not attend weekly religious services compared with those who do, is 1.22.
For those who do not attend weekly religious services compared with those who do: a. The increased risk of dying from all causes for men under age 70 is 0.27. b. The relative risk of dying from cancer for men age 701 is 1.00. c. The relative risk of dying from cancer for men under age 70 is 0.74.
According to the United States Centers for Disease Control, from 2005 to 2009 “ the drowning death rate among males (2.07 per 100,000 population) was approximately four times that for females (0.54 per 100,000 population).” a. Express the rate for males as a percentage of the population; then
According to the University of California at Berkeley Wellness Letter (February 1994, p. 1), only 40% of all surgical operations at that time required 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
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
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 researchers
The previous exercise described the relationship between recently firing someone and having a heart attack. a. Refer to the types of studies described in Chapter 5. What type of study is described in the previous exercise? b. Refer to the reasons for relationships listed in Section 11.3. Which do
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, website or journal; collect it yourself. Be sure to get counts of at least 5 in each cell and be sure the individuals
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
The table below shows the partial results of a survey of 500 middle-aged drivers who were asked whether they had ever had a speeding ticket. Specify the number of people who would fall into each cell if there is no relationship between sex and getting a speeding ticket. Explain your reasoning.
For each of the following situations, would a chi-square test based on a 232 table using a level of 0.01 be statistically significant? Justify your answer. a. chi-square statistic 5 1.42 b. chi-square statistic 5 14.2 c. p-value 5 0.02 d. p-value = 0.15
Use software (such as Excel), a calculator, or a website to find the p-value for each of the following chi-square statistics calculated from a 232 table. You may round off your answer to three decimal places. a. chi-square statistic 5 3.17 b. chi-square statistic 5 5.02 c. chi-square statistic 5
The chi-square test described in this chapter can be used for tables with more than two rows and/ or columns. Use software (such as Excel), a calculator, or a website to find the p-value for each of the following chi-square statistics calculated from a table of the specified number of rows and
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
Refer to the previous exercise. In each case, state the null and alternative hypotheses. a. Researchers want to know if there is a relationship between having graduated from college or not and voting in the last presidential election, for all registered voters over age 25. b. Researchers want to
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.
Refer to Example 13.1, investigating the relationship between taking aspirin and risk of heart attack. As shown in Table 12.1 on page 248, 104 of the 11,037 aspirin takers had heart attacks, whereas 189 of the 11,034 placebo takers had them. The hypotheses for this example are already given in this
In Exercise 12 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. (The format is slightly different from the
In a national survey, 1500 randomly selected adults will be asked if they favor or oppose a ban on texting while driving and if they have personally texted while driving during the previous month. Write null and alternative hypotheses about the relationship between the two variables in this
This is a continuation of Exercise 20 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
If a relationship has practical significance, does it guarantee that statistical significance will be achieved in every study that examines it? Explain.
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
This is a continuation of Exercise 25 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.Minitab computed the chi-square statistic as 66.595. Explain what this means about the
This is a continuation of Exercise 27 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
Example 12.4 and Table 12.5 provided the results of a study in Australia showing that the couples in the study had a higher risk of separation if the wife€™s parents had been divorced. The numbers are shown again in the table below. Write appropriate null and alternative hypotheses for
Refer to the previous exercise about the separation status of Australian couples. a. Find the expected counts for the table. b. Calculate the chi-square test statistic. c. Make a conclusion about whether there is a statistically significant relationship between the two variables using a level of
Is it harder to find statistical significance using a test with level 0.05 or a test with level 0.01? In other words, would a test that is statistically significant using 0.05 always be statistically significant using 0.01, would it be the other way around, or does it depend on the situation?
Explain whether each of the following is possible. a. A relationship exists in the observed sample but not in the population from which the sample was drawn. b. A relationship does not exist in the observed sample but does exist in the population from which the sample was drawn. c. A relationship
What population do you think is represented by the sample for this study? Explain.
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 HuntCarter, 2003, p. 1445). a. State the null and
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)” (Slutske,
Refer to the two results given in the previous exercise. State the conclusion that would be made for each of these two results, both in statistical terms and in the context of the situation. Use a level of 0.05
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
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