Social Statistics for a Diverse Society Eighth Edition Solution Manual

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CHAPTER 1—ANSWERS TO EXERCISES1.Once our research question, the hypothesis, and the study variables have been selected, wemove on to the next stage of the research process—measuring and collecting the data. Thechoice of a particular data collection method or instrument depends on our study objective.After our data have been collected, we have to find a systematic way to organize and analyzeour data and set up some set of procedures to decide what we mean.2.a.Democrats and Independents are more likely to support the Affordable Care Act thanRepublicans.b.Whites have greater incomes than any other race. Hispanics have incomes greater thanblacks but less than whites.c.As the number of police in a city increases, the crime rate will decrease.d.Life satisfaction may vary with marital status, with satisfaction higher among married per-sons than those not married.e.Younger adults are more likely to support the legalization of marijuana than older adults.f.Ethnic minority families are more likely to arrange in-home care (vs. formal institutionalcare) for their elderly parents than nonminority families.3.a.Interval-ratiob.Interval-ratioc.Nominald.Ordinale.Nominalf.Interval-ratiog.Ordinal4.a.Discreteb.Continuousf.Continuous5.There are many possible variables from which to choose. Some of the most common selectionsby students will probably be as follows: type of occupation or industry, work experience, andeducational training or expertise. Students should first address the relationship between thesevariables and gender. Students may also consider measuring structural bias or discrimination.

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6.a.Unemployment records could be used to determine the actual number of unemployed; adescriptive statistic based on the population.b.A survey is taken to estimate student opinions about the quality of food; inferentialstatistic.c.National health records can be used to determine the incidence rate of breast canceramong all Asian women, so this would be a descriptive statistic.d.The ratings will be gathered from a survey, so this is inferential.e.A university should be able to report GPA by major, so this is a descriptive statistic basedon the population.f.In theory, the United States records all immigrants to this country. Therefore, the numberof South East Asian immigrants would be a descriptive statistic. However, because of illegalimmigration, surveys are also taken to estimate the total number of legal and unauthorizedimmigrants. In that event, the number of immigrants would be an inferential statistic.7.a.Annual incomeb.Gender—nominal; Number of hours worked per week—interval-ratio; Years of education—interval-ratio; Job title—nominal.c.This is an application of inferential statistics. She is using information based on hersample to predict the annual income of a larger population of young graduates.8.At the nominal level, a simple measure of political participation is whether or not someonevoted in the most recent general election. This variable would be coded either “ yes” or “ no.”At the ordinal level, a composite measure could be constructed of both voting and politicalparty membership, like this:BehaviorCodeDidn’t vote, no membership0Voted, no membership ORMembership, didn’t vote1Voted and membership2These codes are ordinal in scale because the amount of political participation can be rankedfrom high to low. Other possible ordinal variables can be constructed from other sets ofbehaviors, such as working in a candidate’s campaign, signing a petition, and so forth. Thekey points are to create a variable whose values can be ranked and whose values are not on aninterval-ratio scale.At the interval-ratio level, political participation could be measured by the percentage of elec-tions in which a person has voted since becoming eligible to vote or the amount of money aperson donated to political candidates during some specified time period.9.a.Individual age: This variable could be measured as an interval-ratio variable, with actualage in years reported. As discussed in the chapter, interval-ratio variables are the highestlevel of measurement and can also be measured at ordinal or nominal levels.

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b.Annual income: This variable could be measured as an interval-ratio variable, with actualdollar earnings reported.c.Religiosity: This variable could be measured in several ways. For example, as churchattendance, the variable could be ordinal (number of times attended church in a month:every week, at least twice a month, less than two times a month, none at all).d.Student performance: This could be measured as an interval-ratio variable as GPA or test score.e.Social class: This variable is an ordinal variable, with categories low, working, middle, andupper.f.Number of children: This variable could be measured in several ways. As an interval-ratiomeasure, the actual number of children could be reported. As an ordinal measure, thenumber of children could be measured in categories: 0, 1–2, 3–4, 5 or more. This couldalso be a nominal measurement—do you have children? Yes or No.

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CHAPTER 2—ANSWERS TO EXERCISES1.a.Race is a nominal variable. Class is an ordinal variable, since the categories can be ordered.Trauma is an interval variable.b.Frequency Table for RaceRaceFrequency (f)White17Nonwhite13Total (N)30c.White: 17/30=.57%; Nonwhite: 13/30=.432.Frequency and Percentage Distribution Table for ClassClassFrequency (f)Percentage (%)Lower310Working1550Middle1136.7Upper13.3Total (N)30100a.The smallest perceived class group is the upper class, composing only 3.3% of the survey.b.Together, the working and middle class compose 86.7% of the survey.3.Number of TraumasFrequency (f)01511124Total (N)30a.Trauma is an interval or ratio-level variable, since it has a real zero point and a meaningfulnumeric scale.b.People in this survey are more likely to have experienced no traumas last year (50% of thegroup).

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c.The proportion who experienced one or more traumas is calculated by first adding 36.7%and 13.3%=50%. Then, divide that number by 100 to obtain the proportion, 0.50, or halfthe group.4.We use pie charts to visually present these data.Nonwhite43%White57%Lower10%Upper3%Working50%Middle37%5.Support does vary by political party. The majority of strong Democrats (58.1%) andIndependents (66%) agree/strongly agree with the statement. The group with the lowestpercentage of agreement is Strong Republicans at 49%. The percentage disagreeing with thestatement is highest among Strong Republicans (36.7%) compared with 12.3% of StrongDemocrats and 11.3% of Independents.6.a.E-mailHours perWeekFrequencyCumulativeFrequencyPercentage (%)CumulativePercentage(C%)0191919191203920392135213523557557425925956656656570570No traumas50%1 trauma37%2 traumas13%

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E-mailHours perWeekFrequencyCumulativeFrequencyPercentage (%)CumulativePercentage(C%)72722728375375917617610 or more23992399Total9999%b..575 ( 57/ 99) spent 3 hours or less on e-mail per week.c.This group includes 5+2+3+1+23=34 respondents. The proportion is 34/99 or .343.d.This is an interval-ratio variable. The appropriate graphic presentation would be either ahistogram or a line graph.7.The group with the largest increase in voting rates is blacks, from 53% in 1996 to 66.2% in2012. Blacks are the only group that did not experience a decline in voting rates for the yearspresented. Hispanic voting rates exceeded the voting rates for Asians in 2000 and remainedhigher than Asians through 2012. Hispanics and Asians have the lowest voting rates for allgroups. As noted in the exercise, in the 2012 presidential election, blacks had the highestvoting rates for all groups, followed by non-Hispanic whites, Hispanics, and Asians. Whitevoting rates declined by 2% from 2008 to 2012. The highest voting rate for whites was in2004 (67.2%), in 2008 for Hispanics (49.9%) and for Asians (47.6%).8.From 1970 to 2013, European immigrants had the highest increase in the percentage whocompleted at least high school (95−48=47%). During the same time period, immigrantsfrom the Caribbean had the second highest increase (72−36=36%).Since 1970 at least 50% of immigrants from Other Central/South America countries, Asia, andAfrica had achieved at least a high school education. In 2013, at least 66% of immigrants from fiveout of the six reported regions achieved a high school education.Throughout all the years reportedin the table, immigrants from Mexico have the lowest percentage of high school completion.9.If we identify younger Americans as those in the 18 to 24 and 25 to 44 age-groups and olderAmericans in the 45–64, 65–74, and 75 and over categories—the data indicate that as ageincreases, so does the percentage voting in a Presidential election. The group with the high-est percentage of voting is the 65- to 74-year olds, with 73.5% voting. The percentage dropsfor the 75 and over age-group, but is still higher than the reported percentages for the age-groups: 18–24, 25–44, and 45–64.10.Please note:The data are as reported by the Bureau of Justice Statistics. The percentages donot add up to 100%.All Males (%)CumulativePercentage (C%)All Females(%)CumulativePercentage (C%)18–1911.6.620–2411.412.41010.625–2915.427.817.528.130–3416.544.318.646.735–3914.258.514.761.4(Continued)

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All Males (%)CumulativePercentage (C%)All Females(%)CumulativePercentage (C%)40–4412.270.712.874.245–4910.481.110.985.150–548.589.67.792.855–595.294.83.996.760–642.797.51.898.565+2.399.81.299.711.Overall, the highest percentage of smokers are in the 12th-grade category; the lowest are stu-dents in the 8th grade. The highest percentage of daily smokers for all grades is between 1996and 1997 with percentages declining through 2014. (There are no data for 8th and 10th graderspre-1990.) Since 2012, the percentage of students smoking daily was at 10% or below.12.For all racial and Hispanic groups presented in the bar graph, the percentage of uninsuredindividuals decreased from 2013 to 2014. Hispanics have the highest percentage of unin-sured, followed by blacks, Asians, and whites. According to these data, in 2014, more than a1/3 of Hispanics did not have health insurance. The group with the largest decline is non-Hispanic blacks (24.7−17.6=7.1%); the smallest reduction is among non-Hispanic whites(14.5−11.5=3.0%).13.a.For Africa, Asia, Oceania, and Latin America, the largest age-group is 18 to 44 years. ForEurope and North America, the age composition is slightly older; individuals aged 45 to64 years are the largest age-group for both.b.We display the data in a vertical bar graph. We selected a bar graph because country oforigin (the basis of the percentage calculation) is nominal.0102030405060AfricaAsiaEuropeNorth AmericaOceaniaLatin America65+45–6418–44under 18(Continued)

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SPSS SOLUTIONS1.a.The valid number of responses is 990.b.22.3% reported being in excellent health; 7.0% in poor health.c.HEALTH is an ordinal measure. The best way to graphically present it would be in a bargraph.2.a.

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b.Each variable is an ordinal measurement. The higher value (5) indicates strong disagree-ment with the statement (though the label does not appear in our screenshots). Overall,respondents express positive attitudes toward immigrants. Most believe that immigrantsshould have the same education as Americans (19.8+67.4=87.2%agreeorstrongly agreeto the statement), disagree that immigrants undermine American culture (49.1+8.9=58%disagreeorstrongly disagree), and disagree that immigrants take away jobs (35+6.6=41.6%disagreeorstrongly disagree).3.

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a.GOODLIFE is an ordinal measure (a 5-point scale).b.GOODLIFE may vary by respondent’s age, social class, employment status, education,and one’s overall happiness with life. You may want to explore the relationship betweenGOODLIFE and these variables on your own using the GSS data sets.c.This is an ordinal measure and should be presented as a bar graph.4.Students are encouraged to determine on their own how to recode the variable. Studentsshould consider how the years of education indicates attainment of a specific degree, forexample: 12 years=high school graduate or 16 years=college graduate.5.a.Nominal, as a pie chart or bar graph.b.Interval measure, as a histogram or line chart.c.Ordinal measure, as a bar graph.d.Interval measure, as a histogram or line chart.

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CHAPTER 3—ANSWERS TO EXERCISES1.a.Mode=Routine (f=379)b.Median=Routinec.Based on the mode and median for this variable, most respondents indicate that their livesare “routine.”d.A mean score could not be interpreted for this variable. A mean would have no meaningfor a nominal measurement.2.a.Ordinal.b.The mode can be found in two ways: by looking for the (1) highest frequency (f=251) or(2) highest percentage (32.5%)—“strongly agree”.c.The median can be found in two ways: by using either the frequencies column or thecumulative percentages.Using FrequenciesUsing Cumulative PercentagesN+=+=1212387th case773Notice that 50% of the observationsfall in the “agree” cumulativepercentage category.Starting with the frequency in the first category(251), add up the frequencies until you findwhere the 387th case falls.The 387th case fallsat the “agree” category, which is the median.The 50% mark, or the median, islocated in the “agree” category.The data indicate strong support for same-sex marriage. The largest single categoryis “strongly agree”— 32.5%. Combined with the “agree” category (the second largestcategory), more than half of the GSS sample agree that homosexuals should have theright to marry (32.5+25.2=57.7).3.a.Interval ratio. The mode can be found in two ways: by looking either for the highestfrequency (14) or the highest percentage (43.8%). The mode is the category that corre-sponds to the value “40 hours worked last week.” The median can be found in two ways:by using either the frequencies column or the cumulative percentages.

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Using FrequenciesUsing Cumulative PercentagesN+=+=1212th case3216 5.Notice that 34.4% of the observationsfall in or below the “32 hours worked lastweek” category; 78.1% fall in or below the“40 hours worked last week” category.Starting with the frequency in the firstcategory (1), add up the frequencies untilyou find where the 16th and 17th casesfall. Both these cases correspond to thecategory “40 hours worked last week,”which is the median.The 50% mark, or the median, islocated somewhere within the“40 hours worked last week” category.So the median is “40 hours workedlast week.”b.Since the median is merely a synonym for the 50th percentile, we already know that itsvalue is “40 hours worked last week.”25th percentile=(32×0.25)=8th case=30 hours worked last week.75th percentile=(32×0.75)=24th case=40 hours worked last week4.a.The mode category is “very important”,f=136.b.The median can be found in two ways: either by using the frequencies column or by cal-culating the cumulative percentages. The median score is 3—not very important.c.20th percentile=(392×0.20)=78th case=“Very important”80th percentile=(392×0.80)=314th case=“Not important at all”

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5.a.ModeMedianBlackSeldom (f=11)SometimesWhiteEveryday (f=84)Nearly everydayHispanicEverday (f=25)Most daysb.Teens’ breakfast habits vary by race/ethnicity. Out of the three racial/ethnic groups, blackstudents were more likely to report seldom or sometimes eating breakfast. On the otherhand, white and Hispanic students eat breakfast more frequently. The mode for white andHispanic students is everyday.6.The mode can be found by looking for the highest frequency in each column; the mode foreach group is listed below:Males: Working full timeFemales: Working full timeThe median can be found in two ways: either by using the frequencies column or by usingthe cumulative percentages. However, since the problem only gives the frequencies, we’ll usethose to solve for the median.

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MalesFemalesN+=+=1212th case513257N+=+=1212nd case503252Starting with the frequency in the firstcategory (303), add up the frequenciesuntil you find where the 257th case falls.We actually don’t need to do any adding,as both these cases correspond with thefirst category, “Working FullTime.”Starting with the frequency in the firstcategory (263), add up the frequenciesuntil you find where the 252nd case falls.We actually don’t need to do any adding,as both these cases correspond with thefirst category, “Working FullTime.”When using both the mode and the median to estimate participation in the labor force, itappears that there are no substantial differences between males and females.7.We begin by multiplying each household size by its frequency.Household SizeFrequencyFrequency×Y(f Y)138138125261,052322768142008005964806422527191338540921810220TotalN=1,500∑fY=3,857Yf YN===Σ3,8571,5002.57The mean number of people per household is 2.57.8.a.Based on the table, the 90th percentile is in response category “4.”b.The median is “2.”c.The mean is 2.46=1,673/679.d.The distribution is slightly positively skewed; the mean is larger than the median.

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Ideal Number of ChildrenFrequencyFrequency×Y(fY)011011414239579031885644562245115562127214TotalN=679∑fY=1,6739.a.There appear to be a few outliers (i.e., extremely high values); this leads us to believe thatthe distribution is skewed in the positive direction.001002003004005006002468Number of Persons in HouseholdFrequency1012b.The median can be found in two ways: by using either the frequencies column or thecumulative percentages. The data are in frequencies; we’ll use those to solve the median.Because the median (2) is less than the mean (2.57), we can conclude that the distributionis skewed in a positive direction. Our answer to Question 9a is further supported.

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