(a) The correlation between number of married residents and number of unemployed

Problem 1E What is meant by a marginal distribution? What is meant by a conditional distribution?

Problem 3E Explain why we use the term association rather than correlation when describing the relation between two variables in this section.

Problem 4E Explain the idea behind Simpson’s Paradox.

Problem 2E Refer to Table Level of Education Employment Status Did Not Finish High School High School Graduate Some College Bachelor’s Degree or Higher Employed 9,993 34,130 34,067 43,992 Unemployed 1,806 3,838 3,161 2,149 Not in the labor force 19,969 30,246 18,373 16,290 It is constructing a conditional distribution by level of education different from constructing a conditional distribution by employment status? If they are different, explain the difference.

Problem 7E Made in America In a recent Harris Poll, a random sample of adult Americans (18 years and older) was asked, “When you see an ad emphasizing that a product is ‘Made in America,’ are you more likely to buy it, less likely to buy it, or neither more nor less likely to buy it?” The results of the survey, by age group, are presented in the contingency table below 18–34 35–44 45–54 55+ Total More likely 238 329 360 402 1329 Less likely 22 6 22 16 66 Neither more nor less likely 282 201 164 118 765 Total 542 536 546 536 2160 (a) How many adult Americans were surveyed? How many were 55 and older? ________________ (b) Construct a relative frequency marginal distribution. ________________ (c) What proportion of Americans are more likely to buy a product when the ad says “Made in America”? ________________ (d) Construct a conditional distribution of likelihood to buy “Made in America” by age. That is, construct a conditional distribution treating age as the explanatory variable. ________________ (e) Draw a bar graph of the conditional distribution found in part (d). ________________ (f ) Write a couple sentences explaining any relation between likelihood to buy and age.

Problem 6E In Problems (a) Construct a frequency marginal distribution. (b) Construct a relative frequency marginal distribution. (c) Construct a conditional distribution by x. (d) Draw a bar graph of the conditional distribution found in part (c). x1 x2 x3 y1 35 25 20 y2 65 75 80

Problem 9E dParty AffiliationIs there an association between party affiliation and gender? The following data represent the gender and party affiliation of registered voters based on a random sample of 802 adults Female Male Republican 105 115 Democrat 150 103 Independent 150 179 (a) Construct a frequency marginal distribution. ________________ (b) Construct a relative frequency marginal distribution. ________________ (c) What proportion of registered voters considers themselves to be Independent? ________________ (d) Construct a conditional distribution of party affiliation by gender. ________________ (e) Draw a bar graph of the conditional distribution found in part (d). ________________ (f ) Is gender associated with party affiliation? If so, how?

Problem 5E In Problems (a) Construct a frequency marginal distribution. (b) Construct a relative frequency marginal distribution. (c) Construct a conditional distribution by x. (d) Draw a bar graph of the conditional distribution found in part (c). x1 x2 x3 y1 20 25 30 y2 30 25 50

Problem 10E Feelings on AbortionThe Pew Research Center for the People and the Press conducted a poll in which it asked about the availability of abortion. The table is based on the results of the survey High School or Less Some College College Graduate Generally available 90 72 113 Allowed, but more limited 51 60 77 Illegal, with few exceptions 125 94 69 Never permitted 51 14 17 (a) Construct a frequency marginal distribution. ________________ (b) Construct a relative frequency marginal distribution. ________________ (c) What proportion of college graduates feel that abortion should never be permitted? ________________ (d) Construct a conditional distribution of people’s feelings about the availability of abortion by level of education. ________________ (e) Draw a bar graph of the conditional distribution found in part (d). ________________ (f ) Is level of education associated with opinion on the availability of abortion? If so, how?

In a recent Harris Poll, a random sample of adult Americans (18 years and older) was asked, “Given a choice of the following, which one would you most want to be?” Results of the survey, by gender, are given in the contingency table (a) How many adult Americans were surveyed? How many males were surveyed? (b) Construct a relative frequency marginal distribution. (c) What proportion of adult Americans want to be richer? (d) Construct a conditional distribution of desired traits by gender. That is, construct a conditional distribution treating gender as the explanatory variable. (e) Draw a bar graph of the conditional distribution found in part (d). (f ) Write a couple sentences explaining any relation between desired trait and gender.

Problem 11E Health and HappinessThe General Social Survey asksquestions about one’s happiness and health. One would think that health plays a role in one’s happiness. Use the data in the table to determine whether healthier people tend to also be happier. Treat level of health as the explanatory variable Poor Fair Good Excellent Total Not too happy 696 1,386 1,629 732 4,443 Pretty happy 950 3,817 9,642 5,195 19,604 Very happy 350 1,382 4,520 5,095 11,347 Total 1,996 6,585 15,791 11,022 35,394

Smoking Is Healthy? Could it be that smoking actually increases survival rates among women? The following data represent the 20-year survival status and smoking status of 1314 English women who participated in a cohort study from 1972 to 1992. (a) What proportion of the smokers was dead after 20 years? What proportion of the nonsmokers was dead after 20 years? What does this imply about the health consequences of smoking? The data in the table above do not take into account a variable that is strongly related to survival status, age. The data shown next give the survival status of women and their age at the beginning of the study. For example, 14 women who were 35 to 44 at the beginning of the study were smokers and dead after 20 years. (b) Determine the proportion of 18- to 24-year-old smokers who were dead after 20 years. Determine the proportion of 18- to 24-year old nonsmokers who were dead after 20 years. (c) Repeat part (b) for the remaining age groups to create a conditional distribution of survival status by smoking status for each age group. (d) Draw a bar graph of the conditional distribution from part (c). (e) Write a short report detailing your findings.

Problem 14E Treating Kidney StonesResearchers conducted a study to determine which of two treatments, A or B, is more effective in the treatment of kidney stones. The results of their experiment are given in the table Treatment A Treatment B Total Effective 273 289 562 Not effective 77 61 138 Total 350 350 700 (a) Which treatment appears to be more effective? Why? The data in the table above do not take into account the size of the kidney stone. The data shown next indicate the effectiveness of each treatment for both large and small kidney stones Small Stones Large Stones A B A B Effective 81 234 273 55 Not effective 6 36 77 25 (b) Determine the proportion of small kidney stones that were effectively dealt with using treatment A. Determine the proportion of small kidney stones that were effectively dealt with using treatment B. ________________ (c) Repeat part (b) for the large stones to create a conditional distribution of effectiveness by treatment for each stone size. ________________ (d) Draw a bar graph of the conditional distribution from part (c). ________________ (e) Write a short report detailing your findings

Problem 12E Happy in Your Marriage?The General Social Survey asks questions about one’s happiness in marriage. Is there an association between gender and happiness in marriage? Use the data in the table to determine if gender is associated with happiness in marriage. Treat gender as the explanatory variable Male Female Total Very happy 7,609 7,942 15,551 Pretty happy 3,738 4,447 8,185 Not too happy 259 460 719 Total 11,606 12,849 24,455

What is meant by a marginal distribution? What is meant by a conditional distribution?

Refer to Table 9. Is constructing a conditional distribution by level of education different from constructing a conditional distribution by employment status? If they are different, explain the difference.

Explain why we use the term association rather than correlation when describing the relation between two variables in this section

Explain the idea behind Simpsons Paradox.

In Problems 5 and 6, (a) Construct a frequency marginal distribution. (b) Construct a relative frequency marginal distribution. (c) Construct a conditional distribution by x. (d) Draw a bar graph of the conditional distribution found in part (c). x1 x2 x3 y1 20 25 30 y2 30 25 50

In Problems 5 and 6, (a) Construct a frequency marginal distribution. (b) Construct a relative frequency marginal distribution. (c) Construct a conditional distribution by x. (d) Draw a bar graph of the conditional distribution found in part (c).x1 x2 x3 y1 35 25 20 y2 65 75 80

Made in America In a recent Harris Poll, a random sample of adult Americans (18 years and older) was asked, When you see an ad emphasizing that a product is Made in America, are you more likely to buy it, less likely to buy it, or neither more nor less likely to buy it? The results of the survey, by age group, are presented in the contingency table below. 1834 3544 4554 55+ Total More likely 238 329 360 402 1329 Less likely 22 6 22 16 66 Neither more nor less likely 282 201 164 118 765 Total 542 536 546 536 2160 Source: The Harris Poll (a) How many adult Americans were surveyed? How many were 55 and older? (b) Construct a relative frequency marginal distribution. (c) What proportion of Americans are more likely to buy a product when the ad says Made in America? (d) Construct a conditional distribution of likelihood to buy Made in America by age. That is, construct a conditional distribution treating age as the explanatory variable. (e) Draw a bar graph of the conditional distribution found in part (d). (f ) Write a couple sentences explaining any relation between likelihood to buy and age

Desirability Traits In a recent Harris Poll, a random sample of adult Americans (18 years and older) was asked, Given a choice of the following, which one would you most want to be? Results of the survey, by gender, are given in the contingency table. Richer Thinner Smarter Younger None of these Total Male 520 158 159 181 102 1120 Female 425 300 144 81 92 1042 Total 945 458 303 262 194 2162 Source: The Harris Poll (a) How many adult Americans were surveyed? How many males were surveyed? (b) Construct a relative frequency marginal distribution. (c) What proportion of adult Americans want to be richer? (d) Construct a conditional distribution of desired trait by gender. That is, construct a conditional distribution treating gender as the explanatory variable. (e) Draw a bar graph of the conditional distribution found in part (d). (f ) Write a couple sentences explaining any relation between desired trait and gender.

Party Affiliation Is there an association between party affiliation and gender? The following data represent the gender and party affiliation of registered voters based on a random sample of 802 adults. Female Male Republican 105 115 Democrat 150 103 Independent 150 179 Source: Star Tribune Minnesota Poll (a) Construct a frequency marginal distribution. (b) Construct a relative frequency marginal distribution. (c) What proportion of registered voters considers themselves to be Independent? (d) Construct a conditional distribution of party affiliation by gender. (e) Draw a bar graph of the conditional distribution found in part (d). (f ) Is gender associated with party affiliation? If so, how?

Feelings on Abortion The Pew Research Center for the People and the Press conducted a poll in which it asked about the availability of abortion. The table is based on the results of the survey. High School or Less Some College College Graduate Generally available 90 72 113 Allowed, but more limited 51 60 77 Illegal, with few exceptions 125 94 69 Never permitted 51 14 17 Source: Pew Research Center for the People and the Press (a) Construct a frequency marginal distribution. (b) Construct a relative frequency marginal distribution. (c) What proportion of college graduates feel that abortion should never be permitted? (d) Construct a conditional distribution of peoples feelings about the availability of abortion by level of education (e) Draw a bar graph of the conditional distribution found in part (d). (f ) Is level of education associated with opinion on the availability of abortion? If so, how?

Health and Happiness The General Social Survey asks questions about ones happiness and health. One would think that health plays a role in ones happiness. Use the data in the table to determine whether healthier people tend to also be happier. Treat level of health as the explanatory variable. Poor Fair Good Excellent Total Not too happy 696 1,386 1,629 732 4,443 Pretty happy 950 3,817 9,642 5,195 19,604 Very happy 350 1,382 4,520 5,095 11,347 Total 1,996 6,585 15,791 11,022 35,394 Source: General Social Survey

Happy in Your Marriage? The General Social Survey asks questions about ones happiness in marriage. Is there an association between gender and happiness in marriage? Use the data in the table to determine if gender is associated with happiness in marriage. Treat gender as the explanatory variable. Male Female Total Very happy 7,609 7,942 15,551 Pretty happy 3,738 4,447 8,185 Not too happy 259 460 719 Total 11,606 12,849 24,455 Source: General Social Survey

Smoking Is Healthy? Could it be that smoking actually increases survival rates among women? The following data represent the 20-year survival status and smoking status of 1314 English women who participated in a cohort study from 1972 to 1992. Smoking Status Smoker (S) Nonsmoker (NS) Total Dead 139 230 369 Alive 443 502 945 Total 582 732 1314 Source: David R. Appleton et al. Ignoring a Covariate: An Example of Simpsons Paradox. American Statistician 50(4), 1996 (a) What proportion of the smokers was dead after 20 years? What proportion of the nonsmokers was dead after 20 years? What does this imply about the health consequences of smoking? The data in the table above do not take into account a variable that is strongly related to survival status, age. The data shown next give the survival status of women and their age at the beginning of the study. For example, 14 women who were 35 to 44 at the beginning of the study were smokers and dead after 20 years. Age Group 1824 2534 3544 4554 5564 6574 75 or older S NS S NS S NS S NS S NS S NS S NS Dead 2 1 3 5 14 7 27 12 51 40 29 101 13 64 Alive 53 61 121 152 95 114 103 66 64 81 7 28 0 0 (b) Determine the proportion of 18- to 24-year-old smokers who were dead after 20 years. Determine the proportion of 18- to 24-yearold nonsmokers who were dead after 20 years. (c) Repeat part (b) for the remaining age groups to create a conditional distribution of survival status by smoking status for each age group. (d) Draw a bar graph of the conditional distribution from part (c). (e) Write a short report detailing your findings.

Treating Kidney Stones Researchers conducted a study to determine which of two treatments, A or B, is more effective in the treatment of kidney stones. The results of their experiment are given in the table. Treatment A Treatment B Total Effective 273 289 562 Not effective 77 61 138 Total 350 350 700 Source: C. R. Charig, D. R. Webb, S. R. Payne, and O. E. Wickham. Comparison of Treatment Real Calculi by Operative Surgery, Percutaneous Nephrolithotomi, and Extracorporeal Shock Wave Lithoripsy. British Medical Journal 292(6524): 879882. (a) Which treatment appears to be more effective? Why? The data in the table above do not take into account the size of the kidney stone. The data shown next indicate the effectiveness of each treatment for both large and small kidney stones. Small Stones Large Stones A BA B Effective 81 234 273 55 Not effective 6 36 77 25 (b) Determine the proportion of small kidney stones that were effectively dealt with using treatment A. Determine the proportion of small kidney stones that were effectively dealt with using treatment B. (c) Repeat part (b) for the large stones to create a conditional distribution of effectiveness by treatment for each stone size. (d) Draw a bar graph of the conditional distribution from part (c). (e) Write a short report detailing your findings.

New versus Used Car Satisfaction Are you more likely to be satisfied with your automobile purchase when it is new or used? The following data represent the level of satisfaction of the buyer for both new and used cars. New Used Total Not too satisfied 11 25 36 Pretty satisfied 78 79 157 Extremely satisfied 118 85 203 Total 207 189 396 Source: General Social Survey (a) How many were extremely satisfied with their automobile purchase? (b) Construct a relative frequency marginal distribution. (c) What proportion of consumers was extremely satisfied with their automobile purchase? (d) Construct a conditional distribution of satisfaction by purchase type (new or used). (e) Draw a bar graph of the conditional distribution found in part (d). (f ) Do you think that the purchase type (new versus used) is associated with satisfaction?

Unemployment Rates Recessions are an economic phenomenon that are often defined as two consecutive quarters of reduced national output. One measure to assess the severity of a recession is the rate of unemployment. The table shows the number of employed and unemployed residents of the United States at the peak of each recession (in thousands). Recession of 1982 Recession of 2009 Employed 98.9 130.1 Unemployed 11.3 14.5 Source: Bureau of Labor Statistics (a) Determine the unemployment rate for each recession. Which recession appears worse as measured by unemployment rate? Note: Unemployment rate = unemployed/(employed + unemployed). The data in the table above do not account for level of education. The following data show the unemployment rate by level of education for each recession.Recession of 1982 Recession of 2009 Less than high school High school Bachelors degree or higher Less than high school High school Bachelors degree or higher Employed 20.3 58.2 20.4 10.0 76.7 43.4 Unemployed 3.9 6.6 0.8 2.0 10.3 2.2 Source: Bureau of Labor Statistics (b) Determine the unemployment rate for each level of education for both recessions. (c) Draw a bar graph of the conditional distribution from part (b). (d) Write a report that suggests the recession of 2009 is worse than that of 1982.

(a) The correlation between number of married residents and number of unemployed residents in 2008 for the 50 states and Washington, DC, is 0.922. A scatter diagram of the data drawn in MINITAB is shown. What type of relation appears to exist between number of marriages and number unemployed?(b) A lurking variable is in the relation presented in part (a). Use the following correlation matrix to explain how population is a lurking variable. Correlations: Unemployed, Population, Marriages Unemployed Population Population 0.979 Marriages 0.922 0.947 Cell Contents: Pearson correlation (c) The correlation between unemployment rate (number unemployed divided by population size) and marriage rate (number married divided by population size) in 2008 for the 50 states and Washington, DC, is 0.050. A scatter diagram between unemployment rate and marriage rate drawn in MINITAB is shown next. What type of relation appears to exist between unemployment rate and marriage rate? (d) Write a few sentences to explain the danger in using correlation to conclude that a relation exists between two variables without considering lurking variables.

List the eight properties of the linear correlation coefficient.

Analyzing a Newspaper Article In a newspaper article written in the Chicago Tribune on September 29, 2002, it was claimed that poorer school districts have shorter school days. (a) The following scatter diagram was drawn using the data supplied in the article. In this scatter diagram, the response variable is length of the school day (in hours) and the explanatory variable is percent of the population that is Analyzing a Newspaper Article In a newspaper article written in the Chicago Tribune on September 29, 2002, it was claimed that poorer school districts have shorter school days. (a) The following scatter diagram was drawn using the data supplied in the article. In this scatter diagram, the response variable is length of the school day (in hours) and the explanatory variable is percent of the population that is Analyzing a Newspaper Article In a newspaper article written in the Chicago Tribune on September 29, 2002, it was claimed that poorer school districts have shorter school days. (a) The following scatter diagram was drawn using the data supplied in the article. In this scatter diagram, the response variable is length of the school day (in hours) and the explanatory variable is percent of the population that is