Chapter 6 EPSDue 11/06/15

• A ________________ of counts organizes data about two __________________ variables. Values of the row variable label the rows that run across the table, and values of the column variable label the columns that run down the table. Two–way tables are often used to summarize large amounts of information by ________________ outcomes into categories.

• The _________ totals and _______________ totals in a two–way table give the marginal distributions of the two individual variables. It is clearer to present these distributions as _______________ of the table total. Marginal distributions tell us nothing about the relationship between the variables.

• There are ______________sets of conditional distributions for a two–way table: the distributions of the __________ variable for each fixed value of the column variable and the distributions of the ______________ variable for each fixed value of the row variable. Comparing one set of conditional distributions is one way to describe the association between the row and the column variables.

• To find the conditional distribution of the row variable for one specific value of the column variable, look only at that one ___________ in the table. Find each entry in the ______________ as a percent of the _______________ total.

The Pew Internet and American Life Project interviewed several hundred teens (aged 12 to 17). One question asked was, “How often do you take your cell phone to school?” Here is a two–way table of the responses by how permissive the school is with regard to cell phone use:

Exercises 6.8 to 6.16 are based on this table.

6.8 How many individuals are described by this table?

(a)468

(b)612

(c)Need more information

6.9 How many teens from schools that forbid cell phones were among the respondents?

(a)48

(b)150

(c)Need more information

6.10 The percent of teens from schools that forbid cell phones among the respondents was

(a)about 8%.

(b)about 25%.

(c)about 48%.

6.11 Your percent from Exercise 6.10 is part of

(a)the marginal distribution of school permissiveness.

(b)the marginal distribution of the frequency at which a teen brought a cell phone to school.

(c)the conditional distribution of the frequency at which a teen brought a cell phone to school among schools with a given level of permissiveness.

6.12 What percent of teens from schools that forbid cell phones brought their cell phone to school every day?

(a)about 16%

(b)about 21%

(c)about 65%

6.13 Your percent from Exercise 6.12 is part of

(a)the marginal distribution of the frequency at which a teen brought a cell phone to school.

(b)the conditional distribution of school permissiveness among those who brought a cell phone to school every day.

(c)the conditional distribution of the frequency at which a teen brought a cell phone to school among schools that forbid cell phones.

6.14 What percent of those who brought their cell phone to school every day were from schools that forbid cell phones?

(a)about 16%

(b)about 21%

(c)about 65%

6.15 Your percent from Exercise 6.14 is part of

(a)the marginal distribution of the frequency at which a teen brought a cell phone to school.

(b)the conditional distribution of school permissiveness among those who brought a cell phone to school every day.

(c)the conditional distribution of the frequency at which a teen brought a cell phone to school among schools with a given level of permissiveness.

6.16 A bar graph showing the conditional distribution of the frequency at which a teen brought a cell phone to school among schools with a given level of permissiveness would have

(a)3 bars.

(b)4 bars.

(c)12 bars.

6.17 A college looks at the grade point average (GPA) of its full-time and part-time students. Grades in science courses are generally lower than grades in other courses. There are few science majors among part-time students, but many science majors among full-time students. The college finds that full-time students who are science majors have higher GPAs than part-time students who are science majors. Full-time students who are not science majors also have higher GPAs than part-time students who are not science majors. Yet part-time students as a group have higher GPAs than full-time students. This finding is

(a)not possible: if both science and other majors who are full-time have higher GPAs than those who are part-time, then all full-time students together must have higher GPAs than all part-time students together.

(b)an example of Simpson’s paradox: full-time students do better in both kinds of courses but worse overall because they take more science courses.

(c)due to comparing two conditional distributions that should not be compared.

6.18 Is astrology scientific? The University of Chicago’s General Social Survey (GSS) is the nation’s most important social science sample survey. The GSS asked a random sample of adults their opinion about whether astrology is very scientific, sort of scientific, or not at all scientific. Here is a two–way table of counts for people in the sample who had three levels of higher education degrees:

Find the two conditional distributions of degree held: one for those who hold the opinion that astrology is not at all scientific, and one for those who say astrology is very or sort of scientific.

Based on your calculations, describe with a graph and in words the differences between those who say astrology is not at all scientific and those who say it is very or sort of scientific

Marital status and income. We sometimes hear that getting married is good for your career. Table 6.2 presents data from the U.S. Census Bureau that classifies men, ages 45–64, according to marital status and annual income in 2011–12. We include only data on men, ages 45–64, to avoid sex bias and reduce the effect of age.10 Exercises 6.20 to 6.24 are based on these data.

6.20 Marginal distributions. Give (in percents) the two marginal distributions, for marital status and for income. Do each of your two sets of percents add to exactly 100%? If not, why not?

6.21 Percents. What percent of single men have no income? What percent of men with no income are single men?

6.22 Conditional distribution. Give (in percents) the conditional distribution of income level among single men. Should your percents add to 100% (up to roundoff error)? Explain your reasoning.

6.23 Marital status and income. One way to see the relationship is to look at who has no income.

(a)There are 995,000 married men with no income, and 513,000 single men with no income. Explain why these counts by themselves don’t describe the relationship between marital status and job grade.

(b)Find the percent of men in each marital status group who have no income. Then find the percent in each marital group who have an income of $100,000 and over. What do these percents say about the relationship?

6.24 Association is not causation. The data in Table 6.2 show that single men are more likely to hold lower-income jobs than are married men. We should not conclude that single men can increase their income by getting married. What lurking variables might help explain the association between marital status and income?