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Statistics Chapter 3: Smoking and Education - KEY 200 adults shopping at a supermarket were asked about the highest level of education they had completed and whether or not they smoke cigarettes. Results are summarized in the table High school 2 yr college 4+ yr college Total 1. Smoker 32 5 13 50 Non-smoker 61 17 72 150 Total 93 22 85 200 Discuss the W’s. Who: 200 adults. What: education level and smoking habits When: not specified Where: shopping mall How: not specified. Was this a random sample, or were some people simply asked? Why: to examine possible links between smoking and education level 2. Identify the variables. Categorical variables: Education level, and whether or not the person was a smoker. 3. Find each percent requested below. d) What percent of the shoppers were smokers with only high school educations? e) What percent of the shoppers with only high school educations were smokers? f) What percent of the smokers had only high school educations? 4. 32 200 32 93 = 16% ≈ 34.4% 32 50 = 64% Do these data suggest there is an association between smoking and education level? Give statistical evidence to support your conclusion. These data provide evidence of an association between smoking and education level. 64% of smokers had only a high school diploma, while only 40.7% of non-smoker had only high school diplomas. Only 26% of smokers had four or more years of college, compared to 48% of smokers. 5. Follow-up question: Does this indicate that students who start smoking while in high school tend to give up the habit if they complete college? Explain. These data do not indicate that students who start smoking in high school tend to give up the habit if they complete college. These data were gathered at one time, about two different groups, smokers and nonsmokers. We have no idea if smoking behavior changes over time. Copyright © 2012 Pearson Education, Inc. Publishing as Addison-Wesley. 3-12 7. Why do the column totals equal 100%, but the row totals do not? Major Major 1. 2. 3. 4. 5. 6. Statistics Chapter 3: Review A – KEY Birth Order 1 2 3 4+ Total 34 14 6 3 57 Math/Science 52 27 5 9 93 Agriculture 15 17 8 3 43 Humanities 12 11 1 6 30 Other 113 69 20 21 223 Total What percent of these students are oldest or only children? 113/223 = 51% What percent of the Humanities majors are oldest children? 15/43 = 35% What percent of oldest children are Humanities students? 15/113 = 13% What percent of the students are oldest children majoring in the Humanities? 15/223 = 7% Find the marginal distribution of majors. 26% Math/Sci, 42% Ag, 19% Humanities, 13% Other Complete this table showing the conditional relative distribution of majors for each birth order. Birth Order 1 2 3 4+ 20% 14% 30% 30% Math/Science 46% 39% 25% 43% Agriculture 25% 13% 40% 14% Humanities 29% 11% 16% 5% Other 100% 100% 100% 100% Total We are finding the conditional distribution of major within each birth order, not the other way around. 8. Do you think choice of major is independent of birth order? Use statistics to justify your reasoning. No, there appears to be an association between major and birth order. The conditional distributions of major by birth order are different. 9. Examine the pie graphs below and explain how they provide evidence to support or refute your answer to question 8. The pie charts provide support to the association between major and birth order. The pie charts show a different distribution of major for each birth order. If major and birth order were independent, we would expect each pie chart to show a similar distribution. Copyright © 2012 Pearson Education, Inc. Publishing as Addison-Wesley. 3-14 Statistics Chapter 3: Review B – KEY Age The Pew Research Center conducts surveys regularly asking respondents which political party they identify with. Among their results is the following table relating prefer political party and age (http://people-press.org/reports/) Party Republican Democrat Others Total 2636 2738 4765 10139 18-29 6871 6442 8160 21473 30-49 3896 4286 4806 12988 50-64 3131 3718 2934 9784 65+ 16535 17183 20666 54384 Total 1. Identify the variables, tell their possible values, and identify each variable as categorical or quantitative. Party – Categorical variable with values Republican, Democrat, Other Age – Categorical variable with values 18 – 29, 30 – 49, 50 – 64, and 65+. 2. Identify the W’s of this study. Which W’s are unknown? Who – Not specified (probably US residents) What – Party and age range. Where – Not specified (Probably US) When – Not specified. Why – Opinion polling How – Survey. 3. What percent of people surveyed were Republicans? 16535/54384 = 30.4% 4. What percent of people surveyed were under 30 or over 65? (10139+3131)/54384 = 24.4% 5. What percent of the people classified as “Other” were under 30? 4765/20666 = 23.1% 6. What percent of the people under 30 were classified as “Other”? 4765/10139 = 47.0% 7. What is the marginal distribution of ages? 18.6% of the respondents were 18 – 29 years old, 39.5% were 30 – 49, 23.9% were 50 – 64 and 18.0% were over 65 years old. 8. Find the conditional relative frequency of ages among democrats. 15.9% of the Democrats were 18 – 29 years old, 37.5% were 30 – 49, 24.9% were 50 – 64 and 21.6% were over 65 years old. 9. Do you think party affiliation is independent of age? Give statistical evidence to support your conclusion. There is some evidence of an association between party affiliation and age. Although the conditional distributions of age (from youngest to oldest) for the Democrats (15.9%, 37.5%, 24.9%, 21.6%) and Republicans (15.9%, 41.6%, 23.6%, 18.9%) were similar, the conditional distribution of age for the Other category (23.1%, 39.5%, 23.3%, 14.2%) showed a slightly higher percentage of younger respondents and a slightly lower percentage of older respondents than the two main political parties. Copyright © 2012 Pearson Education, Inc. Publishing as Addison-Wesley. 3-16 Statistics Chapter 3: Review C – KEY Bus Ride Personal Total Male 30 37 19 86 Female 34 45 23 102 Total 64 82 42 188 In order to plan transportation and parking needs at a private high school, administrators asked students how they get to school. Some rode a school bus, some rode in with parents or friends, and others used “personal” transportation – bikes, skateboards, or just walked. The table summarizes the responses from boys and girls. 1. Identify the variables and tell whether each is categorical or quantitative. Gender and mode of transportation, both categorical. 2. Which of the W’s are unknown for these data? We don’t know how or when the students were surveyed, nor where the school is. 3. 4. Find each percent. a. What percent of the students are girls who ride the bus? b. What percent of the girls ride the bus? c. What percent of the bus riders are girls? 18.1% 33.3% 53.1% Identify the marginal distribution of gender. There are 86 males and 102 females 5. Write a sentence or two about the conditional relative frequency distribution of modes of transportation for the boys. More boys (43%) caught rides to school than any other means of transportation. 35% rode the bus while only 22% used personal transportation like biking, skateboarding, or walking. 6. Do you think mode of transportation is independent of gender? Give statistical evidence to support your conclusion. The way students get to school does seem to be independent of gender. Overall, 34% of students ride the bus, compared to 35% of the boys and 33% of the girls. 44% of all students caught rides with someone and 22% used personal transportation, almost the same as the percentages for boys (43% and 22%) or girls (44% and 23%) separately. These data provide little indication of a difference in mode of transportation between boys and girls at this school Copyright © 2012 Pearson Education, Inc. Publishing as Addison-Wesley. 3-18