Sullivan Statistics Survey In the Sullivan Statistics Survey, respondents were asked to

True or False: The expected frequencies in a chi-square test for independence are found using the formula Expected frequency = (row total)(column total) table total

In a chi-square test for of proportions, we test whether different populations have the same proportion of individuals with some characteristic.

The following table contains observed values and expected values in parentheses for two categorical variables, X and Y, where variable X has three categories and variable Y has two categories: X1 X2 X3 Y1 34 (36.26) 43 (44.63) 52 (48.11) Y2 18 (15.74) 21 (19.37) 17 (20.89) (a) Compute the value of the chi-square test statistic. (b) Test the hypothesis that X and Y are independent at the a = 0.05 level of significance.

The table in the next column contains observed values and expected values in parentheses for two categorical variables, X and Y, where variable X has three categories and variable Y has two categories. X1 X2 X3 Y1 87 (75.12) 74 (80.43) 34 (39.46) Y2 12 (23.88) 32 (25.57) 18 (12.54) (a) Compute the value of the chi-square test statistic. (b) Test the hypothesis that X and Y are independent at the a = 0.05 level of significance.

The following table contains the number of successes and failures for three categories of a variable. Category 1 Category 2 Category 3 Success 76 84 69 Failure 44 41 49 Test whether the proportions are equal for each category at the a = 0.01 level of significance.

The following table contains the number of successes and failures for three categories of a variable. Category 1 Category 2 Category 3 Success 204 199 214 Failure 96 121 98

Family Structure and Sexual Activity A sociologist wants to discover whether the sexual activity of females between the ages of 15 and 19 years of age and family structure are associated. She randomly selects 380 females between the ages of 15 and 19 years of age and asks each to disclose her family structure at age 14 and whether she has had sexual intercourse. The results are shown in the table. Data are based on information obtained from the U.S. National Center for Health Statistics. Family Structure Had Sexual Intercourse Both Biological or Adoptive Parents Single Parent Parent and Stepparent Nonparental Guardian Yes 64 59 44 32 No 86 41 36 18 (a) Compute the expected values of each cell under the assumption of independence. (b) Verify that the requirements for performing a chi-square test of independence are satisfied. (c) Compute the chi-square test statistic. (d) Test whether family structure and sexual activity of 15- to 19-year-old females are independent at the a = 0.05 level of significance. (e) Compare the observed frequencies with the expected frequencies. Which cell contributed most to the test statistic? Was the expected frequency greater than or less than the observed frequency? What does this information tell you? (f) Construct a conditional distribution by family structure and draw a bar graph. Does this evidence support your conclusion in part (d)?

Prenatal Care An obstetrician wants to learn whether the amount of prenatal care and the wantedness of the pregnancy are associated. He randomly selects 939 women who had recently given birth and asks them to disclose whether their pregnancy was intended, unintended, or mistimed. In addition, they were to disclose when they started receiving prenatal care, if ever. The results of the survey are as follows: Months Pregnant before Prenatal Care Began Wantedness of Pregnancy Less Than 3 Months 3 to 5 Months More Than 5 Months (or never) Intended 593 26 33 Unintended 64 8 11 Mistimed 169 19 16 (a) Compute the expected values of each cell under the assumption of independence. (b) Verify that the requirements for performing a chi-square test of independence are satisfied. (c) Compute the chi-square test statistic. (d) Test whether prenatal care and the wantedness of pregnancy are independent at the a = 0.05 level of significance. (e) Compare the observed frequencies with the expected frequencies. Which cell contributed most to the test statistic? Was the expected frequency greater than or less than the observed frequency? What does this information tell you? (f) Construct a conditional distribution by wantedness of the pregnancy and draw a bar graph. Does this evidence support your conclusion in part (d)?

Health and Happiness Are health and happiness related? The following data represent the level of happiness and level of health for a random sample of individuals from the General Social Survey. Health Excellent Good Fair Poor Very Happy 271 261 82 20 Happiness Pretty Happy 247 567 231 53 Not Too Happy 33 103 92 36 Source: General Social Survey (a) Does the evidence suggest that health and happiness are related? Use the a = 0.05 level of significance. (b) Construct a conditional distribution of happiness by level of health and draw a bar graph. (c) Write a few sentences that explain the relation, if any, between health and happiness.

Health and Education Does amount of education play a role in the healthiness of an individual? The following data represent the level of health and the highest degree earned for a random sample of individuals from the General Social Survey. Health Excellent Good Fair Poor Less than High School 72 202 199 62 Education High School 465 877 358 108 Junior College 80 138 49 11 Bachelor 229 276 64 12 Graduate 130 147 32 2 Source: General Social Survey (a) Does the evidence suggest that health and education are related? Use the a = 0.05 level of significance. (b) Construct a conditional distribution of health by level of education and draw a bar graph. (c) Write a few sentences that explain the relation, if any, between health and education. Can you think of any lurking variables that help to explain the relation between these two variables?

Profile of Smokers The following data represent the smoking status by level of education for residents of the United States 18 years old or older from a random sample of 1054 residents.Smoking Status Number of Years of Education Current Former Never 612 178 88 208 12 137 69 143 1315 44 25 44 16 or more 34 33 51 Source: National Health Interview Survey (a) Test whether smoking status and level of education are independent at the a = 0.05 level of significance. (b) Construct a conditional distribution of smoking status by number of years of education, and draw a bar graph. Does this evidence support your conclusion in part (a)?

Pro Life or Pro Choice A recent Gallup organization poll asked male and female Americans whether they were pro life or pro choice when it comes to abortion issues. The results of the survey are as follows: Pro Life/Pro Choice Gender Pro Life Pro Choice Men 196 199 Women 239 249 (a) Test whether an individuals opinion regarding abortion is independent of gender at the a = 0.1 level of significance. (b) Construct a conditional distribution of abortion opinion by gender and draw a bar graph. Does this evidence support your conclusion in part (a)?

Equal Opportunity Do you believe everyone has an equal opportunity to obtain a quality education in the United States? The results of this General Social Survey question are presented next by level of education. Highest Degree Less Than High School High School Junior College Bachelor Graduate Yes 302 551 29 100 46 No 83 200 24 71 31 Source: General Social Survey (a) Does the evidence suggest that the proportion of individuals who feel everyone has an equal opportunity to obtain a quality education in the United States is equal for each level of education? Use the a = 0.05 level of significance. (b) Construct a conditional distribution of opinion by level of education and draw a bar graph of the conditional distribution. What role does education appear to play in beliefs about access to quality education?

Celebrex Celebrex, a drug manufactured by Pfizer, Inc., is used to relieve symptoms associated with osteoarthritis and rheumatoid arthritis in adults. In clinical trials of the medication, some subjects reported dizziness as a side effect. The researchers wanted to discover whether the proportion of subjects taking Celebrex who reported dizziness as a side effect differed significantly from that for other treatment groups. The following data were collected. Drug Side Effect Celebrex Placebo Naproxen Diclofenac Ibuprofen Dizziness 83 32 36 5 8 No dizziness 4063 1832 1330 382 337 Source: Pfizer, Inc. (a) Test whether the proportion of subjects within each treatment group who experienced dizziness are the same at the a = 0.01 level of significance. (b) Construct a conditional distribution of side effect by treatment and draw a bar graph. Does this evidence support your conclusion in part (a)?

Whats in a Word? In a recent survey conducted by the Pew Research Center for the People & the Press, a random sample of adults 18 years of age or older living in the continental United States was asked their reaction to the word socialism. In addition, the individuals were asked to disclose which political party they most associate with. Results of the survey are given in the table. Democrat Independent Republican Positive 220 144 62 Negative 279 410 351 Source: Pew Research (a) Does the evidence suggest a different proportion of individuals within each political affiliation reacts positively to the word socialism? Use the a = 0.05 level of significance. (b) Construct a conditional distribution of reaction by political party. (c) Write a summary about the partisan divide regarding reaction to the word socialism.

Whats in a Word? Part II In a recent survey conducted by the Pew Research Center for the People & the Press, a random sample of adults 18 years of age or older living in the continental United States was asked their reaction to the word capitalism. In addition, the individuals were asked to disclose which political party they most associate with. Results of the survey are given in the table. Democrat Independent Republican Positive 235 288 256 Negative 264 266 157 Source: Pew Research (a) Does the evidence suggest a different proportion of individuals within each political affiliation reacts positively to the word capitalism? Use the a = 0.05 level of significance. (b) Construct a conditional distribution of reaction by political party. (c) Write a summary about the partisan divide regarding reaction to the word capitalism. (d) Compare the results of this problem with that of Problem 15. Write a short report detailing the findings of the two survey questions.

Dropping a Course A survey of 52 randomly selected students who dropped a course in the current semester was conducted at a community college. The goal of the survey was to learn why students drop courses. The following data were collected: Personal drop reasons include financial, transportation, family issues, health issues, and lack of child care. Course drop reasons include reducing ones load, being unprepared for the course, the course was not what was expected, dissatisfaction with teaching, and not getting the desired grade. Work drop reasons include an increase in hours, a change in shift, and obtaining fulltime employment. The results of the survey are as follows: Gender Drop Reason Gender Drop Reason Male Personal Male Work Female Personal Male Work Male Work Female Course Male Personal Male Work Male Course Female Course Male Course Female Course Female Course Female Course Female Course Male Work Male Course Male Personal Female Course Male Course Male Personal Female Course Male Work Female Course Male Work Male Course Male Course Female Course Male Course Male Work Male Work Male Course Female Personal Female Work Male Course Male Personal Female Work Male Work Male Work Female Course Male Work Male Course Female Course Male Personal Female Personal Female Course Female Personal Female Work Female Personal Male Work (a) Construct a contingency table for the two variables. (b) Test whether gender is independent of drop reason at the a = 0.1 level of significance. (c) Construct a conditional distribution of drop reason by gender and draw a bar graph. Does this evidence support your conclusion in part (b)?

Political Affiliation A political scientist wanted to learn whether there is any association between the education level of a registered voter and his or her political party affiliation. He randomly selected 46 registered voters and obtained the following data: Education Political Party Education Political Party Grade school Democrat High school Democrat College Republican College Republican High school Democrat College Republican High school Republican Grade school Democrat High school Democrat High school Republican Grade school Democrat High school Democrat College Republican High school Democrat Grade school Democrat College Republican High school Democrat High school Republican High school Democrat Grade school Democrat Grade school Democrat High school Democrat College Republican College Democrat Grade school Democrat College Republican College Democrat High school Republican College Democrat College Democrat Grade school Republican College Democrat College Republican High school Democrat Grade school Republican College Republican College Republican College Democrat High school Democrat High school Republican College Democrat College Republican College Republican High school Republican College Democrat College Democrat (a) Construct a contingency table for the two variables. (b) Test whether level of education is independent of political affiliation at the a = 0.1 level of significance. (c) Construct a conditional distribution of political party by level of education and draw a bar graph. Does this evidence support your conclusion in part (b)?

Sullivan Statistics Survey In the Sullivan Statistics Survey, respondents were asked to disclose their political affiliation (Democrat, Independent, Republican) and also answer the following question: Would you be willing to pay higher taxes if the tax revenue went directly toward deficit reduction? Create a contingency table and determine whether the results suggest there is an association between political affiliation and willingness to pay higher taxes to directly reduce the federal debt. Use the a = 0.05 level of significance.

Sullivan Statistics Survey In the Sullivan Statistics Survey, respondents were asked to disclose their political philosophy (Conservative, Moderate, Liberal) and also answer the following question: Is a language other than English the primary language spoken in your home? Create a contingency table and determine whether the results suggest there is an association between political philosophy and whether a language other than English is primarily spoken at home. Use the a = 0.05 level of significance.

Putting It Together: Women, Aspirin, and Heart Attacks In a famous study by the Physicians Health Study Group from Harvard University from the late 1980s, 22,000 healthy male physicians were randomly divided into two groups; half the physicians took aspirin every other day, and the others were given a placebo. Of the physicians in the aspirin group, 104 heart attacks occurred; of the physicians in the placebo group, 189 heart attacks occurred. The results were statistically significant, which led to the advice that males should take an aspirin every other day in the interest of reducing the chance of having a heart attack. Does the same advice apply to women? In a randomized, placebo-controlled study, 39,876 healthy women 45 years of age or older were randomly divided into two groups. The women in group 1 received 100 mg of aspirin every other day; the women in group 2 received a placebo every other day. The women were monitored for 10 years to determine if they experienced a cardiovascular event (such as heart attack or stroke). Of the 19,934 in the aspirin group, 477 experienced a heart attack. Of the 19,942 women in the placebo group, 522 experienced a heart attack. Source: Paul M. Ridker et al. A Randomized Trial of Low-Dose Aspirin in the Primary Prevention of Cardiovascular Disease in Women. New England Journal of Medicine 352:12931304. (a) What is the population being studied? What is the sample? (b) What is the response variable? Is it qualitative or quantitative? (c) What are the treatments? (d) What type of experimental design is this? (e) How does randomization deal with the explanatory variables that were not controlled in the study? (f) Determine whether the proportion of cardiovascular events in each treatment group is different using a two-sample Z-test for comparing two proportions. Use the a = 0.05 level of significance. What is the test statistic? (g) Determine whether the proportion of cardiovascular events in each treatment group is different using a chi-square test for homogeneity of proportions. Use the a = 0.05 level of significance. What is the test statistic? (h) Square the test statistic from part (f) and compare it to the test statistic from part (g). What do you conclude?

Explain the differences between the chi-square test for independence and the chi-square test for homogeneity. What are the similarities?

Why does the test for homogeneity follow the same procedures as the test for independence?