Problem 9
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 10
The Chance article about the Houston magnet schools program described in Exercise 9 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).
Problem 11
The Centers for Disease Control and Prevention (www.cdc.gov) lists causes of death in the United States during 2004: $$ \begin{array}{l|c} \text { Cause of Death } & \text { Percent } \\ \hline \text { Heart disease } & 27.2 \\ \text { Cancer } & 23.1 \\ \text { Circulatory diseases and stroke } & 6.3 \\ \text { Respiratory diseases } & 5.1 \\ \text { Accidents } & 4.7 \end{array} $$ a) Is it reasonable to conclude that heart or respiratory diseases were the cause of approximately \(33 \%\) of U.S. deaths in \(2003 ?\) b) What percent of deaths were from causes not listed here? c) Create an appropriate display for these data.
Problem 12
An investigation compiled information about recent nonmilitary plane crashes (www. planecrashinfo.com). The causes, to the extent that they could be determined, are summarized in the table. $$ \begin{array}{l|c} \text { Cause } & \text { Percent } \\ \hline \text { Pilot error } & 40 \\ \text { Other human error } & 5 \\ \text { Weather } & 6 \\ \text { Mechanical failure } & 14 \\ \text { Sabotage } & 6 \end{array} $$ a) Is it reasonable to conclude that the weather or mechanical failures caused only about \(20 \%\) of recent plane crashes? b) In what percent of crashes were the causes not determined? c) Create an appropriate display for these data.
Problem 14
Twenty-six countries won medals in the 2006 Winter Olympics. The table lists them, along with the total number of medals each won: $$ \begin{array}{l|c|l|c} \text { Country } & \text { Medals } & \text { Country } & \text { Medals } \\\ \hline \text { Germany } & 29 & \text { Finland } & 9 \\ \text { United States } & 25 & \text { Czech Republic } & 4 \\ \text { Canada } & 24 & \text { Estonia } & 3 \\ \text { Austria } & 23 & \text { Croatia } & 3 \\ \text { Russia } & 22 & \text { Australia } & 2 \\ \text { Norway } & 19 & \text { Poland } & 2 \\ \text { Sweden } & 14 & \text { Ukraine } & 2 \\ \text { Switzerland } & 14 & \text { Japan } & 1 \\ \text { South Korea } & 11 & \text { Belarus } & 1 \\ \text { Italy } & 11 & \text { Bulgaria } & 1 \\ \text { China } & 11 & \text { Great Britain } & 1 \\ \text { France } & 9 & \text { Slovakia } & 1 \\ \text { Netherlands } & 9 & \text { Latvia } & 1 \end{array} $$ a) Try to make a display of these data. What problems do you encounter? b) Can you find a way to organize the data so that the graph is more successful?
Problem 17
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. $$ \begin{array}{l|c|c} \text { Brand preference } & \text { South } & \text { West } \\ \hline \text { Marlboro } & 58.4 \% & 58.0 \% \\ \text { Newport } & 22.5 \% & 10.1 \% \\ \text { Camel } & 3.3 \% & 9.5 \% \\ \text { Other (over 20 brands) } & 9.1 \% & 9.5 \% \\ \text { No usual brand } & 6.7 \% & 12.9 \% \end{array} $$
Problem 18
In an effort to reduce the number of gunrelated 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 on the next page 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. $$ \begin{array}{l|c|c} \text { Caliber of gun } & \text { Buyback } & \text { Homicide } \\ \hline \text { Small }(.22, .25, .32) & 76.4 \% & 20.3 \% \\ \text { Medium }(.357, .38,9 \mathrm{~mm}) & 19.3 \% & 54.7 \% \\ \text { Large }(.40, .44, .45) & 2.1 \% & 10.8 \% \\ \text { Other } & 2.2 \% & 14.2 \% \end{array} $$
Problem 20
Here's another table showing information about 120 movies released in 2005 . This table gives percentages of the table total: a) How can you tell that this table holds table percentages (rather than row or column percentages)? b) What was the most common genre/rating combination in 2005 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 three-quarters of the movies made today can be seen only by patrons 13 years old or older." Does this table support that assertion? Explain.
Problem 35
The following table shows the number of licensed U.S. drivers by age and by sex (www.dot.gov): $$ \begin{array}{l|rr|r} \text { Age } & \begin{array}{c} \text { Male Drivers } \\ \text { (number) } \end{array} & \begin{array}{c} \text { Female Drivers } \\ \text { (number) } \end{array} & \text { Total } \\ \hline 19 \text { and under } & 4,777,694 & 4,553,946 & \mathbf{9 , 3 3 1 , 6 4 0} \\ 20-24 & 8,611,161 & 8,398,879 & \mathbf{1 7 , 0 1 0 , 0 4 0} \\ 25-29 & 8,879,476 & 8,666,701 & \mathbf{1 7 , 5 4 6 , 1 7 7} \\ 30-34 & 9,262,713 & 8,997,662 & \mathbf{1 8 , 2 6 0 , 3 7 5} \\ 35-39 & 9,848,050 & 9,576,301 & \mathbf{1 9 , 4 2 4 , 3 5 1} \\ 40-44 & 10,617,456 & 10,484,149 & \mathbf{2 1 , 1 0 1 , 6 0 5} \\ 45-49 & 10,492,876 & 10,482,479 & \mathbf{2 0 , 9 7 5 , 3 5 5} \\ 50-54 & 9,420,619 & 9,475,882 & \mathbf{1 8 , 8 9 6 , 5 0 1} \\ 55-59 & 8,218,264 & 8,265,775 & \mathbf{1 6 , 4 8 4 , 0 3 9} \\ 60-64 & 6,103,732 & 6,147,569 & \mathbf{1 2 , 2 5 1 , 3 6 1} \\ 65-69 & 4,571,157 & 4,643,913 & \mathbf{9 , 2 1 5 , 0 7 0} \\ 70-74 & 3,617,908 & 3,761,039 & \mathbf{7 , 3 7 8 , 9 4 7} \\ 75-79 & 2,890,155 & 3,192,408 & \mathbf{6 , 0 8 2 , 5 6 3} \\ 80-84 & 1,907,743 & 2,222,412 & \mathbf{4 , 1 3 0 , 1 5 5} \\ 85 \text { and over } & 1,170,817 & 1,406,271 & \mathbf{2 , 5 7 7 , 0 8 8} \\ \hline \text { Total } & \mathbf{1 0 0 , 3 8 9 , 8 8 1} & \mathbf{1 0 0 , 2 7 5 , 3 8 6} & \mathbf{2 0 0 , 6 6 5 , 2 6 7} \end{array} $$ 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 40
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 \(\mathrm{A}\). 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.
