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Statistical Methods For The Social Sciences 5th Edition Alan Agresti - Solutions
Look at Figure 2 at http://ajph.aphapublica tions.org/doi/pdf/10.2105/AJPH.93.4.652, a scatterplot for U.S. states with correlation 0.53 between x = child poverty rate and y = child mortality rate.Approximate the y-intercept and slope of the prediction equation shown there.
The OECD (Organization for Economic Cooperation and Development) consists of advanced, industrialized countries. For these nations, a recent prediction equation6 relating y = child poverty rate to x = social expenditure as a percentage of gross domestic product isˆy = 22 − 1.3x. The y-values
Anthropologists often try to reconstruct information using partial human remains at burial sites. For instance, after finding a femur (thighbone), they may want to predict how tall an individual was. An equation they use to do this is ˆy = 61.4 + 2.4x, where ˆy is the predicted height and x is
Sketch plots of the following prediction equations, for values of x between 0 and 10:(a) ˆy = 7 + x, (b) ˆy = 7 − x, (c) ˆy = 7, (d) ˆy = x.
For the following variables in a regression analysis, which variable more naturally plays the role of x (explanatory variable) and which plays the role of y (response variable)?(a) College grade point average (GPA) and high school GPA.(b) Number of children and mother’s education level.(c) Annual
The annual UCLA survey of college freshmen13 indicated that 82% of college freshmen in 2014 considered being financially well-off to be essential or very important, compared to 42% when the survey was first conducted in 1966. Are the sample percentages of 42% in 1966 and 82%in 2014 based on
Transatlantic Trends is an annual survey of American and European public opinion (http://trends.gmfus.org), with a random sample of about 1000 adults from each of 13 European countries each year. In 2006, 18% of Europeans expressed a positive attitude about President George W. Bush’s handling of
The National Health Interview Survey (www.cdc.gov/nchs) estimated that current cigarette smokers were 42% of American adults in 1965 and 20% in 2014.(a) Estimate the difference between the proportions who smoked in the two years.(b) Suppose the standard error were reported as 0.020 for each
When a recent Eurobarometer survey asked subjects in each European Union country whether they would be willing to pay more for energy produced from renewable sources than for energy produced from other sources, the proportion answering yes varied from a high of 0.52 in Denmark (n = 1008) to a low
The National Center for Health Statistics recently estimated that the mean weight for adult American women was 140 pounds in 1962 and 166 pounds in 2010.(a) Suppose these estimates had standard errors of 2 pounds each year. Estimate the increase in mean weight in the population from 1962 to 2010,
The U.S. Census Bureau estimated that the median net worth in the United States in 2013 was $142,000 for white households and $11,000 for black households.(a) Identify the response variable and the explanatory variable.(b) Compare the groups using a (i) difference, (ii) ratio.
In 2013, the U.S. Department of Justice reported that the incarceration rate in the nation’s prisons was 1191 per 100,000 adult male residents (composed of 3% of black males and 0.5% of white males), and 83 per 100,000 female residents.(a) Find the ratio of the proportions of incarceration, for
According to the U.S. National Center for Health Statistics, the annual probability that a male between the ages of 20 and 24 is a homicide victim is 0.00164 for blacks and 0.00015 for whites.(a) Compare these rates using the difference of proportions.(b) Compare these rates using the ratio of
TheWorldValues Survey14 asked, “How often do you pray?” The response never was given by 16.5% of the 2232 respondents in the United States and by 44.5% of the 1477 respondents in Australia.(a) Assuming random sampling, the 95% confidence interval for the difference between corresponding
For a random sample of Canadians, 60% indicate approval of the prime minister’s performance. A similar poll a month later has a favorable rating of 57%. A 99%confidence interval for the change in the population proportions is (−0.07, 0.01). Explain why (a) there may have been no change in
The College Alcohol Study at the Harvard School of Public Health has interviewed random samples of students at four-year colleges several times since 1993. In the most recent study, of the students who reported drinking alcohol, the percentage who reported that drinking “to get drunk” is an
The study mentioned in the previous exercise estimated in 1993 that 19.2% had engaged in unplanned sexual activities because of drinking alcohol; this was 21.3%at the latest survey.(a) Specify assumptions, notation, and hypotheses for a two-sided test comparing the corresponding population
In Great Britain, the Time Use Survey(www.statistics.gov.uk) studied how a random sample of Brits spend their time on a typical day. Of those working full time, 55% of 1219 men and 74% of 733 women reported spending some time on cooking and washing up during a typical day. Find and interpret a
Table 7.14 summarizes responses from General Social Surveys in 1977 and in 2014 to the statement “It is much better for everyone involved if the man is the achiever outside the home and the woman takes care of the home and family.” Let π1 denote the population proportion who agreed with this
Refer to the previous exercise. In 2014, of 745 male respondents, 247 (33.2%) agreed. Of 910 female respondents, 268 (29.5%) agreed.(a) Set up notation and specify hypotheses for the hypothesis of no difference between the population proportions of males and of females who would agree.(b) Estimate
In a survey conducted by Wright State University, senior high school students were asked if they had ever used marijuana. Table 7.15 shows software output. Treating these observations as a random sample from the population of interest,(a) State a research question that could be addressed with this
A study of compulsive buying behavior (uncontrolled urges to buy) conducted a national telephone survey in 2004 of adults ages 18 and over.15 Of 800 men, 44 were judged to be compulsive buyers according to the Compulsive Buying Scale. Of 1501 women, 90 were judged to be compulsive buyers. Conduct
Table 7.16 shows results from the 2014 General Social Survey on belief in an afterlife, classified by sex. Conduct all steps of a significance test, using α = 0.05, to compare the population proportions of females and males who would respond yes to belief in an afterlife. If you have made an error
A GSS reported that the 486 females had a mean of 8.3 close friends (s = 15.6) and the 354 males had a mean of 8.9 close friends (s = 15.5).(a) A 95% confidence interval for the difference between the population means for males and for females is (−1.5, 2.7). Interpret.(b) For each sex, does it
Table 7.17 summarizes the number of hours spent in housework per week by gender, based on a recent GSS.(a) Estimate the difference between the population means for women and men.(b) Show that the estimated standard error of the sample difference is 0.81.Interpret.(c) Show that a 99% confidence
A 30-month study evaluated the degree of addiction that teenagers form to nicotine once they begin experimenting with smoking.16 The study used a random sample of 332 seventh-grade students in two Massachusetts cities who had ever used tobacco by the start of the study. The response variable was
In Great Britain, the Time Use Survey17 studied how a random sample of Brits spend their time on a typical day. For those who reported working full time, Table 7.18 reports the mean and standard deviation of the reported average number of minutes per day spent on cooking and washing up.(a) Estimate
A recent General Social Survey asked, “How many days in the past 7 days have you felt sad?” Software reported sample means of 1.8 for females and 1.4 for males, with a 95% confidence interval comparing them of (0.2, 0.6), a t statistic of 4.8, and a P-value of 0.000.Interpret these results.
For the 2014 General Social Survey, a comparison of females and males on the number of hours a day that the subject watched TV gave----------------------------------------------Group n Mean StdDev Std Error Mean Females 916 2.94 2.60 0.086 Males 753 3.03 2.57 0.094
For the 2014 GSS, Table 7.19 shows software output for evaluating the number of hours of TV watching per day by race.(a) Interpret the reported confidence interval. Can you conclude that one population mean is higher? If so, which one? Explain.(b) Interpret the reported P-value.(c) Explain the
In a study18 comparing various drink types (alcohol, energy drink, alcohol plus energy, decaffeinated soda) on college students’ desire for additional drinks after various lengths of time, the soda drink had the least effect. In one analysis for the soda, the authors reported that desire ratings
In a study19 of the effect of the compound tomoxetine as a treatment for adult attention deficit hyperactivity disorder (ADHD), the 21 subjects had an ADHD rating scale mean of 30.0 (s = 6.7) at baseline and 21.5 (s = 10.1)after three weeks of treatment. The standard deviation was 9.84 for the 21
As part of her class project, a student at the University of Florida randomly sampled 10 fellow students to investigate their most common social activities. As part of the study, she asked the students to state how many times they had done each of the following activities during the previous year:
Interpret the 95% confidence interval shown.(c) Show how the test statistic shown in the output was obtained from the other information given. Report the P-value, and interpret in context.
Refer to the previous exercise. For comparing parties and sports, software reports a 95% confidence interval of (−3.33, 28.93) and a P-value of 0.106.Explain the connection between the results of the significance test and the confidence interval.
Aclinical psychologist wants to choose between two therapies for treating mental depression. For six patients, she randomly selects three to receive therapy A, and the other three receive therapy B. She selects small samples for ethical reasons; if her experiment indicates that one therapy is
Refer to the previous exercise. To avoid bias from the samples being unbalanced with such small n, the psychologist redesigned the experiment. She forms three pairs of subjects, such that the patients matched in any given pair are similar in health and socioeconomic status. For each pair, she
A study20 of treatments for obesity for rural women examined the impact of a six-month behavioral weight loss program delivered by phone either one-on-one with a counselor or to a group via conference call. A sample of rural women classified as obese by their BMI were randomly assigned to the two
For the survey of students described in Exercise 1.11, the responses on political ideology had a mean of 3.18 and standard deviation of 1.72 for the 51 nonvegetarian students and a mean of 2.22 and standard deviation of 0.67 for the 9 vegetarian students. When we use software to compare the means
In 2014, the General Social Survey asked about the number of hours a week spent on the World Wide Web, not counting e-mail. The 778 females had a mean of 11.2 and standard deviation of 13.7.The 620 males had a mean of 11.9 and standard deviation of 16.0.Use these results to make an inference
Two new short courses have been proposed for helping students who suffer from severe math phobia, scoring at least 8 on a measure of math phobia that falls between 0 and 10 (based on responses to 10 questions). A sample of 10 such students were randomly allocated to the two courses. Following the
Recent years have seen impressive improvements in systems for automatically recognizing speech. Research in comparing the quality of different speech recognition systems often uses as a benchmark test a series of isolated words, checking how often each system makes errors recognizing the word.
A General Social Survey asked subjects their opinions about government spending on health and on law enforcement. Table 7.26 shows results.(a) Find the sample proportion favoring increased spending, for each item.(b) Test whether the population proportions are equal.Report the P-value, and
The World Values Survey has asked if homosexuality is justifiable, on a scale from 1 (“never”) to 10 (“always”).In 1981–1984 surveys in the United States of 2325 subjects, 62.4% gave response 1. In 2010–2014 surveys of 2232 respondents, 24.0% gave response 1. A report claimed that this
An experimental study22 of young children’s moral behavior used as subjects 32 three-year-old girls, half assigned to each of two conditions. Each girl and two actors created a picture or clay sculpture, after which one actor left the room. In the Harm condition, the remaining actor then
In a study about lesbianism, 45 young adults were asked whether they had ever had a same-gender sexual relationship. Table 7.28 shows results. Use software to test whether the probability of this is higher for those raised by lesbian mothers. Interpret.
For the Students data file (Exercise 1.11 on page 9), use graphical and numerical summaries and inferential statistical methods for the following:(a) Compare political ideology of students identifying as Democrats and as Republicans.(b) Compare opinions of males and females about legalized
For the data file created in Exercise 1.12, with variables chosen by your instructor, state a research question and conduct inferential statistical analyses. Prepare a report that summarizes your findings. In this report, also use graphical and numerical methods to describe the data.
Using the Comparing Two Means applet at www.artofstat.com/webapps.html, construct two scenarios of independent samples of four men and four women with y = number of hours spent on Internet in past week having ¯y1 = 5 and ¯y2 = 10, such that for testing H0: μ1 = μ2 against Ha: μ1 = μ2, (a)
Exercise 3.6 on page 58 showed data on carbon dioxide emissions, a major contributor to global warming, for advanced industrialized nations. State a research question for these data that involves comparing means or proportions. Conduct an investigation to answer this question.
Pose null and alternative hypotheses about the relationship between time spent on the Internet (variable WWWHR for the GSS) and a binary explanatory that you believe may be associated with Internet use. Using the most recent GSS data on these variables at sda.berkeley.edu/GSS, conduct the test.
Browse one or two daily online newspapers such as The New York Times. Find an article about a research study that compared two groups. Prepare a short report that answers the following questions:(a) What was the purpose of the research study?(b) Identify explanatory and response variables.(c) Can
A study23 considered whether greater levels of TV watching by teenagers were associated with a greater likelihood of committing aggressive acts over the years. The researchers randomly sampled 707 families in two counties in northern New York State and made follow-up observations over 17 years.
According to an article in The New York Times (December 6, 2015), the number of annual gun homicides per million people is 31.2 in the United States, 5.6 in Canada, 2.3 in the Netherlands, 0.9 in England, and 0.1 in Japan.Show an informative way to compare these rates between the United States and
The World Values Survey asks if homosexuality is justifiable, on a scale from 1 (“never”) to 10 (“always”).In 1981–1984 surveys, the 2325 respondents in the United States had a mean response of 2.4 and standard deviation of 2.3.In 2010–2014 surveys, the 2232 U.S. respondents had a mean
The results in Table 7.29 are from a study24 of physical attractiveness and subjective well-being. A sample of college students were rated by a panel on their physical attractiveness. The table presents the number of dates in the past three months for students rated in the top or bottom quartile of
In the World Values Survey, interviews of 1902 subjects in the Netherlands found that 29.2% reported having confidence in the European Union and 33.0% reported having confidence in the government of the Netherlands.Do you have enough information to make an inferential comparison of the percentages?
In 2011, the United States Supreme Court dealt with a sex discrimination case in which women managers at Walmart earned $14,500 a year less, on the average, than their male counterparts. If you were also given the standard errors of the annual mean salaries for male and female managers at Walmart,
The International Adult Literacy Survey25 was a 22-country study in which nationally representative samples of adults were interviewed and tested at home, using the same literacy test having scores that could range from 0 to 500. For those of age 16–25, some of the mean prose literacy scores were
Table 7.30 compares two hospitals on the outcomes of patient admissions for severe pneumonia. Although patient status is an ordinal variable, two researchers who analyze the data treat it as an interval variable. The first researcher assigns the scores (0, 5, 10) to the three categories.The second
From Example 6.4 (page 148), for the cognitive behavioral therapy group the sample mean change in weight of 3.0 pounds was significantly different from 0. However, Example 7.8 (page 194) showed it is not significantly different from the mean change for the control group, even though that group had
A survey by the Harris Poll of 2250 Americans in 2013 indicated that 42% believe in ghosts, 26% believe in witches, 29% believe in astrology, and 36% believe in creationism.(a) Is it valid to compare the proportions using inferential methods for independent samples? Explain.(b) Doyou have enough
A pool of six candidates for three managerial positions includes three females and three males. Table 7.31 shows the results.(a) Denote the three females by F1, F2, and F3 and the 3 males by M1, M2, and M3. Identify the 20 distinct samples of size three that can be chosen from these six
Describe a situation in which it would be more sensible to compare means using dependent samples than independent samples.
An AP story about a University of Chicago survey of 1600 people of ages 15 to 25 in several Midwest U.S.cities indicated that 58% of black youth, 45% of Hispanic youth, and 23% of white youth reported listening to rap music every day.(a) True or false: If a 95% confidence interval comparing the
True or false? If a 95% confidence interval for(μ2 − μ1) contains only positive numbers, then we can conclude that both μ1 and μ2 are positive.
True or false? If you know the standard error of the sample mean for each of two independent samples, you can figure out the standard error of the difference between the sample means, even if you do not know the sample sizes.In Exercises 7.62–7.64, select the correct response(s). More than one
A99% confidence interval for the difference π2−π1 between the proportions of men and women in California who are alcoholics equals (0.02, 0.09).(a) We are 99% confident that the proportion of alcoholics is between 0.02 and 0.09.(b) We are 99% confident that the proportion of men in California
To compare the population mean annual incomes for Hispanics (μ1) and for whites (μ2) having jobs in construction, we construct a 95% confidence interval forμ2 − μ1.(a) If the confidence interval is (3000, 6000), then at this confidence level we conclude that the population mean income is
The Wilcoxon test differs from parametric procedures comparing means in the sense that(a) It applies directly to ordinal as well as interval response variables.(b) It is unnecessary to assume that the population distribution is normal.(c) Random sampling is not assumed.
A test consists of 100 true–false questions. Joe did not study, so on each question he randomly guesses the correct response.(a) Find the probability that he scores at least 70, thus passing the exam. (Hint: Use either the binomial distribution or the sampling distribution for the proportion of
Table 8.30 exhibits the maximum possible association between two binary variables for a sample of size n.(a) Show that X2 = n for this table and, hence, that the maximum value of X2 for 2 × 2 tables is n.(b) The phi-squared measure of association for 2×2 contingency tables has sample valueExplain
For a 2×2 table with cell countsa, b,c, d, the sample log odds ratio logˆθ has approximately a normal sampling distribution with estimated standard errorThe antilogs of the endpoints of the confidence interval for log(θ) are endpoints of the confidence interval for θ.For Table 8.14 on page
In an ordinal table, to calculate the number of concordant pairs C, start at the corner of the table for the low level for each variable. Multiply that cell count by the count in every cell that is higher on both variables. Similarly, for every other cell, multiply the cell count by the counts in
A chi-squared variable with degrees of freedom equal to df has representation z21+ · · · + z2 df, where z1, . . . , zdf are independent standard normal variates.(a) If z is a test statistic that has a standard normal distribution, what distribution does z2 have?(b) Explain how to get the
Construct a 3×3 table for which gamma equals (a)1, (b) −1, (c) 0.
For 2×2 tables, gamma simplifies to a measure first proposed about 1900 by the British statistician G. Udny Yule, who also introduced the odds ratio. In that special case, gamma is called Yule’s Q.(a) Show that for a generic table with counts (a,b) in row 1 and (c,d) in row 2, the number of
Each subject in a sample of 100 men and 100 women is asked to indicate which of the following factors (one or more) are responsible for increases in crime committed by teenagers: A—the increasing gap in income between the rich and poor, B—the increase in the percentage of single-parent
The correct answer in Exercise 8.38(c) implies that if the chi-squared statistic is used for a contingency table having ordered categories in both directions, then (select the correct response(s))(a) The statistic actually treats the variables as nominal.(b) Information about the ordering is
Answer true or false for the following. Explain your answer.(a) Even when the sample conditional distributions in a contingency table are only slightly different, when the sample size is very large it is possible to have a large X2 test statistic and a very small P-value for testing H0:
(a) When the sample size is very large, we have not necessarily established an important result when we show a statistically significant association. Explain.(b) The remarks in Sections 8.3 and 8.4 about small Pvalues not necessarily referring to an important effect apply for any significance test.
Shortly before a gubernatorial election, a poll asks a random sample of 50 potential voters the following questions:Party: Do you consider yourself to be a Democrat (D), a Republican (R), or an Independent (I)?Vote: If you were to vote today, would you vote for the Democratic candidate (D) or the
An abstract of an article6 dealing with alcohol use and sexual assault among college women stated,“This study prospectively examined the relation between alcohol use and sexual assault in a sample (n = 319) of first-year college women. ... Over the course of their freshman year, 19.3% reported
For 2014 GSS data, of those identifying as Democrats, 496 classified themselves as liberal and 171 as conservative. Of those identifying as Republicans, 56 called themselves liberal and 499 conservative. Using methods of this chapter, describe the strength of association, and interpret.
Does belief in evolution vary according to religious beliefs? Examine this using Table 8.28, for respondents to the 2014 General Social Survey. The variables are Fundamentalism/Liberalism of Respondent’s Religion and response to whether human beings developed from earlier species of animals.
Pose a research question about attitude regarding homosexual relations and political ideology. Using the most recent GSS data on variables HOMOSEX and POLVIEWS, conduct a descriptive and inferential analysis to address this question. Prepare a one-page report summarizing your analysis.
One year the GSS asked how housework was shared between the respondent and his or her spouse. Possible responses were 1 = I do much more than my fair share, 2 =I do a bit more than my fair share, 3 = I do roughly my fair share, 4 = I do a bit less than my fair share, 5 = I do much less than my fair
Refer to the data file you created in Exercise 1.12.For variables chosen by your instructor, pose a research question and conduct descriptive and inferential statistical analyses. Interpret and summarize your findings in a short report.
Refer to the Students data file (Exercise 1.11 on page 9). Using software, create and analyze descriptively and inferentially the contingency table relating opinion about abortion and (a) political affiliation, (b) religiosity.
Refer to Exercise 8.13 on happiness and income.The analysis there does not take into account the ordinality of the variables. Using software, summarize the strength of association by finding and interpreting gamma.Construct inference using it, and interpret.Concepts and Applications
A GSS cross-classified income in thousands of dollars(25) by job satisfaction (very dissatisfied, a little satisfied, moderately satisfied, very satisfied)for black Americans. Software provides the results shown in Table 8.26.(a) Interpret theP-value reported for the chi-squared test.(b) Conduct an
For the 2014 GSS, γˆ = 0.19 for the relationship between job satisfaction (categories very dissatisfied, little dissatisfied, moderately satisfied, very satisfied) and family income (below average, average, above average).(a) Would you consider this a very strong or relatively weak association?
Table 8.25 cross-classifies happiness with family income for the subsample of the 2014 GSS that identified themselves as Jewish.(a) Give an example of a (i) concordant pair, (ii) discordant pair.(b) The table has 204 concordant pairs and 55 discordant pairs. Find gamma, and interpret.(c) Show how
According to a 2015 study by the Pew Research Center (www.people-press.org), the percentage of Americans who favor allowing gays and lesbians to marry legally was 81% for Democrats who identified themselves as liberal and 22% for Republicans who identified themselves as conservative.(a) The odds
Refer to Table 8.1 (page 216) on political party ID and gender. Find and interpret the odds ratio for each 2×2 subtable. Explain why this analysis suggests that the last two columns show a very weak association.
According to the U.S. Bureau of Justice Statistics, in 2014 the incarceration rate in the nation’s prisons was 904 per 100,000 male residents, 65 per 100,000 female residents, 2805 per 100,000 black residents, and 466 per 100,000 white residents. (Source: www.bjs.gov.)(a) Find the odds ratio
The 2012 National Survey on Drug Use and Health(NSDUH) estimated that 23% of Americans aged 12 or over reported binge drinking in the past month, and 7%had used marijuana in the past month.(a) Find the odds of (i) binge drinking, (ii) marijuana use.Interpret.(b) Find the odds ratio comparing binge
Table 8.24 cross-classifies 68,694 passengers in autos and light trucks involved in accidents in the state of Maine by whether they were wearing a seat belt and by whether they were injured or killed. Describe the association using(a) The difference between two proportions, treating whether injured
In a survey of senior high school students inDayton, Ohio, 1449 students had used both alcohol and cigarettes, 281 had used neither, 500 had used alcohol but not cigarettes, and 46 had used cigarettes but not alcohol.(a) Construct the 2 × 2 table relating alcohol use to cigarette use. Describe the
In a recent GSS, the death penalty for subjects convicted of murder was favored by 74% of whites and 43%of blacks. It was favored by 75% of males and 63% of females.In this sample, which variable was more strongly associated with death penalty opinion—race, or gender?Explain why.
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