Tattoos A study by the University of Texas Southwestern

Problem 7E Graphs in the news Find a bar chart of categorical data from a newspaper, a magazine, or the Internet. a) Is the graph clearly labeled? b) Does it violate the area principle? c) Does the accompanying article tell the W’s of the variable? d) Do you think the article correctly interprets the data? Explain.

Graphs in the news II Find a pie chart of categorical data from a newspaper, a magazine, or the Internet. a) Is the graph clearly labeled? b) Does it violate the area principle? c) Does the accompanying article tell the W’s of the variable? d) Do you think the article correctly interprets the data? Explain.

Problem 9E Tables in the news Find a frequency table of categorical data from a newspaper, a magazine, or the Internet. a) Is it clearly labeled? b) Does it display percentages or counts? c) Does the accompanying article tell the W’s of the variable? d) Do you think the article correctly interprets the data? Explain.

Tables in the news II Find a contingency table of categorical data from a newspaper, a magazine, or the Internet. a) Is it clearly labeled? b) Does it display percentages or counts? c) Does the accompanying article tell the W’s of the variables? d) Do you think the article correctly interprets the data? Explain.

Movie genres II The pie chart summarizes the genres of 193 movies shown in a suburban multiplex theatre in 2012. a) Is this an appropriate display for the genres? Why or why not? b) Which genre was least common?

Problem 16E Magnet schools again The Chance article about the Houston magnet schools program described in Exercise also indicated that 517 applicants were black or Hispanic, 292 Asian, and 946 white. Summarize the relative frequency distribution of ethnicity with a sentence or two (in the proper context, of course). Exercise Magnet schools An article in the Winter 2003 issue of Chance magazine reported on the Houston Independent School District’s magnet schools programs. Of the 1755 qualified applicants, 931 were accepted, 298 were waitlisted, and 526 were turned away for lack of space. Find the relative frequency distribution of the decisions made, and write a sentence describing it.

Problem 15E Magnet schools An article in the Winter 2003 issue of Chance magazine reported on the Houston Independent School District’s magnet schools programs. Of the 1755 qualified applicants, 931 were accepted, 298 were waitlisted, and 526 were turned away for lack of space. Find the relative frequency distribution of the decisions made, and write a sentence describing it.

Problem 20E Winter Olympics 2010 Twenty-six countries won medals in the 2010 Winter Olympics. The table lists them, along with the total number of medals each won: a) Try to make a display of these data. What problems do you encounter? b) Organize the data so that the graph is more successful.

Problem 22E Modalities A survey of athletic trainers (Source: Scott F. Nadler, Michael Prybicien, Gerard A. Malanga, and Dan Sicher, “Complications from Therapeutic Modalities: Results of a National Survey of Athletic Trainers.” Archives of Physical Medical Rehabilitation 84 [June 2003]) asked what modalities (treatment methods such as ice, whirlpool, ultrasound, or exercise) they commonly use to treat injuries. Respondents were each asked to list three modalities. The article included the following figure reporting the modalities used: a) What problems do you see with the graph? b) Consider the percentages for the named modalities. Do you see anything odd about them?

Problem 13E Genres again Here is a bar chart summarizing the 2012 movie genres from the suburban multiplex theatre, as seen in the pie chart in Exercise 11. a) Were Action/Adventure or SciFi/Fantasy films more common? b) Is it easier to see that in a pie chart or the bar chart? Explain. Exercise 11: Movie genres II The pie chart summarizes the genres of 193 movies shown in a suburban multiplex theatre in 2012. a) Is this an appropriate display for the genres? Why or why not? b) Which genre was least common?

Problem 23E Teen smokers The organization Monitoring the Future (www.monitoringthefuture.org) asked 2048 eighth graders who said they smoked cigarettes what brands they preferred. The table below shows brand preferences for two regions of the country. Write a few sentences describing the similarities and differences in brand preferences among eighth graders in the two regions listed. Brand Preference South West Marlboro 58.4% 58.0% Newport 22.5% 10.1% Camel 3.3% 9.5% Other (over 20 brands) 9.1% 9.5% No usual brand 6.7% 12.9%

Problem 21E Global warming The Pew Research Center for the People and the Press (people-press.org) has asked a representative sample of U.S. adults about global warming, repeating the question over time. In October 2010, the responses reflected a decreased belief that global warming is real and due to human activity. Here’s a display of the percentages of respondents choosing each of the major alternatives offered: List the errors in this display.

Problem 24E Handguns In an effort to reduce the number of gun-related homicides, some cities have run buyback programs in which the police offer cash (often $50) to anyone who turns in an operating handgun. Chance magazine looked at results from a four-year period in Milwaukee. The table below shows what types of guns were turned in and what types were used in homicides during a four-year period. Write a few sentences comparing the two distributions. Caliber of Gun Buyback Homicide Small (.22, .25, .32) 76.4% 20.3% Medium (.357, .38, 9 mm) 19.3% 54.7% Large (.40, .44, .45) 2.1% 10.8% Other 2.2% 14.2%

Movies by genre and rating Here’s a table that classifies movies released in a year by genre and MPAA rating: a) The table gives column percents. How could you tell that from the table itself? b) What percentage of these movies were comedies? c) What percentage of the PG-rated movies were comedies? d) Which of the following can you learn from this table? Give the answer if you can find it from the table. i. The percentage of PG-13 movies that were comedies ii. The percentage of dramas that were R-rated iii. The percentage of dramas that were G-rated iv. The percentage of movies that were PG-rated comedies

Problem 28E Politics Students in an Intro Stats course were asked to describe their politics as “Liberal,” “Moderate,” or “Conservative.” Here are the results: a) What percent of the class is male? ________________ b) What percent of the class considers themselves to be “Conservative”? ________________ c) What percent of the males in the class consider themselves to be “Conservative”? ________________ d) What percent of all students in the class are males who consider themselves to be “Conservative”?

Problem 26E The last picture show Here’s another table showing information on 348 movies released in 2010. This table gives percentages of the overall total: a) How can you tell that this table holds overall percentages (rather than row or column percentages)? b) What was the most common genre/rating combination in 2010 movies? c) How many of these movies were PG-rated comedies? d) How many were G-rated? e) An editorial about the movies noted, “More than threequarters of the movies made today can be seen only by patrons 13 years old or older.” Does this table support that assertion? Explain.

Seniors Prior to graduation, a high school class was surveyed about its plans. The following table displays the results for white and minority students (the “Minority” group included African-American, Asian, Hispanic, and Native American students): a) What percent of the seniors are white? b) What percent of the seniors are planning to attend a 2-year college? c) What percent of the seniors are white and planning to attend a 2-year college? d) What percent of the white seniors are planning to attend a 2-year college? e) What percent of the seniors planning to attend a 2-year college are white?

Politics revisited Look again at the table of political views for the Intro Stats students in Exercise 28. a) Find the conditional distributions (percentages) of political views for the females. b) Find the conditional distributions (percentages) of political views for the males. c) Make a graphical display that compares the two distributions. d) Do the variables Politics and Sex appear to be independent? Explain

Problem 29E Pizza prices again Look again at the histogram of the pizza prices in Exercise. a) Is the mean closer to $2.40, $2.60, or $2.80? Why? ________________ b) Is the standard deviation closer to $0.15, $0.50, or $1.00? Explain. Exercise Pizza prices The histogram shows the distribution of the prices of plain pizza slices (in $) for 156 weeks in Dallas, TX. Which summary statistics would you choose to summarize the center and spread in these data? Why?

Problem 31E Magnet schools revisited The Chance magazine article described in further examined the impact of an applicant’s ethnicity on the likelihood of admission to the Houston Independent School District’s magnet schools programs. Those data are summarized in the table below: a) What percent of all applicants were Asian? ________________ b) What percent of the students accepted were Asian? ________________ c) What percent of Asians were accepted? ________________ d) What percent of all students were accepted?

Problem 34E Cars A survey of autos parked in student and staff lots at a large university classified the brands by country of origin, as seen in the table. a) What percent of all the cars surveyed were foreign? ________________ b) What percent of the American cars were owned by students? ________________ c) What percent of the students owned American cars? ________________ d) What is the marginal distribution of origin? ________________ e) What are the conditional distributions of origin by driver classification? ________________ f) Do you think that the origin of the car is independent of the type of driver? Explain.

Weather forecasts Just how accurate are the weather forecasts we hear every day? The following table compares the daily forecast with a city’s actual weather for a year: a) On what percent of days did it actually rain? b) On what percent of days was rain predicted? c) What percent of the time was the forecast correct? d) Do you see evidence of an association between the type of weather and the ability of forecasters to make an accurate prediction? Write a brief explanation, including an appropriate graph.

Problem 32E More politics Look once more at the table summarizing the political views of Intro Stats students in Exercise 28 a) Produce a graphical display comparing the conditional distributions of males and females among the three categories of politics. b) Comment briefly on what you see from the display in part a. Exercise 28: Politics Students in an Intro Stats course were asked to describe their politics as “Liberal,” “Moderate,” or “ Conservative.” Here are the results: a) What percent of the class is male? b) What percent of the class considers themselves to be “Conservative”? c) What percent of the males in the class consider themselves to be “Conservative”? d) What percent of all students in the class are males who consider themselves to be “Conservative”?

Back to school Examine the table about ethnicity and acceptance for the Houston Independent School District’s magnet schools program, shown in Exercise 31. Does it appear that the admissions decisions are made independent of the applicant’s ethnicity? Explain.

Problem 38E Obesity and exercise The Centers for Disease Control and Prevention (CDC) has estimated that 19.8% of Americans over 15 years old are obese. The CDC conducts a survey on obesity and various behaviors. Here is a table on selfreported exercise classified by body mass index (BMI): a) Are these percentages column percentages, row percentages, or table percentages? ________________ b) Use graphical displays to show different percentages of physical activities for the three BMI groups. ________________ c) Do these data prove that lack of exercise causes obesity? Explain.

Problem 36E Twins In 2000, the Journal of the American Medical Association (JAMA) published a study that examined pregnancies that resulted in the birth of twins. Births were classified as preterm with intervention (induced labor or cesarean), preterm without procedures, or term/post-term. Researchers also classified the pregnancies by the level of prenatal medical care the mother received (inadequate, adequate, or intensive). The data, from the years 1995–1997, are summarized in the table on the next page. Figures are in thousands of births. (JAMA 284 [2000]:335–341) a) What percent of these mothers received inadequate medical care during their pregnancies? ________________ b) What percent of all twin births were preterm? ________________ c) Among the mothers who received inadequate medical care, what percent of the twin births were preterm? ________________ d) Create an appropriate graph comparing the outcomes of these pregnancies by the level of medical care the mother received. ________________ e) Write a few sentences describing the association between these two variables.

Problem 39E Anorexia Hearing anecdotal reports that some patients undergoing treatment for the eating disorder anorexia seemed to be responding positively to the antidepressant Prozac, medical researchers conducted an experiment to investigate. They found 93 women being treated for anorexia who volunteered to participate. For one year, 49 randomly selected patients were treated with Prozac and the other 44 were given an inert substance called a placebo. At the end of the year, patients were diagnosed as healthy or relapsed, as summarized in the table: Do these results provide evidence that Prozac might be helpful in treating anorexia? Explain.

Problem 37E Blood pressure A company held a blood pressure screening clinic for its employees. The results are summarized in the table below by age group and blood pressure level: a) Find the marginal distribution of blood pressure level. ________________ b) Find the conditional distribution of blood pressure level within each age group. ________________ c) Compare these distributions with a segmented bar graph. ________________ d) Write a brief description of the association between age and blood pressure among these employees. ________________ e) Does this prove that people’s blood pressure increases as they age? Explain.

Problem 40E Antidepressants and bone fractures For a period of five years, physicians at McGill University Health Center followed more than 5000 adults over the age of 50. The researchers were investigating whether people taking a certain class of antidepressants (SSRIs) might be at greater risk of bone fractures. Their observations are summarized in the table: Do these results suggest there’s an association between taking SSRI antidepressants and experiencing bone fractures? Explain.

Drivers’ licenses 2011 The table on the next page shows the number of licensed U.S. drivers (in millions) by age and by sex (www.dot.gov). a) What percent of total drivers are under 20? b) What percent of total drivers are male? c) Write a few sentences comparing the number of male and female licensed drivers in each age group. d) Do a driver’s age and sex appear to be independent? Explain.

Problem 42E Tattoos A study by the University of Texas Southwestern Medical Center examined 626 people to see if an increased risk of contracting hepatitis C was associated with having a tattoo. If the subject had a tattoo, researchers asked whether it had been done in a commercial tattoo parlor or elsewhere. Write a brief description of the association between tattooing and hepatitis C, including an appropriate graphical display. Tattoo Done in Commercial Parlor Tattoo Done Elsewhere No Tattoo Has Hepatitis C 17 8 18 No Hepatitis C 35 53 495

Problem 46E Be a Simpson Can you design a Simpson’s paradox? Two companies are vying for a city’s “Best Local Employer” award, to be given to the company most committed to hiring local residents. Although both employers hired 300 new people in the past year, Company A brags that it deserves the award because 70% of its new jobs went to local residents, compared to only 60% for Company B. Company B concedes that those percentages are correct, but points out that most of its new jobs were full-time, while most of Company A’s were part-time. Not only that, says Company B, but a higher percentage of its full-time jobs went to local residents than did Company A’s, and the same was true for part-time jobs. Thus, Company B argues, it’s a better local employer than Company A. Show how it’s possible for Company B to fill a higher percentage of both full-time and part-time jobs with local residents, even though Company A hired more local residents overall.

Problem 45E Graduate admissions A 1975 article in the magazine Science examined the graduate admissions process at Berkeley for evidence of sex discrimination. The table below shows the number of applicants accepted to each of four graduate programs: a) What percent of total applicants were admitted? ________________ b) Overall, was a higher percentage of males or females admitted? ________________ c) Compare the percentage of males and females admitted in each program. ________________ d) Which of the comparisons you made do you consider to be the most valid? Why?

Problem 44E Delivery service A company must decide which of two delivery services it will contract with. During a recent trial period, the company shipped numerous packages with each service and kept track of how often deliveries did not arrive on time. Here are the results: Delivery Service Type of Service Number of Deliveries Number of Late Packages Pack Rats Regular Overnight 400 100 12 16 Boxes R Us Regular Overnight 100 400 2 28 a) Compare the two services’ overall percentage of late deliveries. ________________ b) On the basis of the results in part a, the company has decided to hire Pack Rats. Do you agree that Pack Rats delivers on time more often? Explain. ________________ c) The results here are an instance of what phenomenon?

Problem 43E Hospitals Most patients who undergo surgery make routine recoveries and are discharged as planned. Others suffer excessive bleeding, infection, or other postsurgical complications and have their discharges from the hospital delayed. Suppose your city has a large hospital and a small hospital, each performing major and minor surgeries. You collect data to see how many surgical patients have their discharges delayed by postsurgical complications, and you find the results shown in the following table. a) Overall, for what percent of patients was discharge delayed? ________________ b) Were the percentages different for major and minor surgery? ________________ c) Overall, what were the discharge delay rates at each hospital? ________________ d) What were the delay rates at each hospital for each kind of surgery? ________________ e) The small hospital advertises that it has a lower rate of postsurgical complications. Do you agree? ________________ f) Explain, in your own words, why this confusion occurs.