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Statistics The Art And Science Of Learning From Data 3rd Edition Alan Agresti, Christine A. Franklin - Solutions

A study of the death penalty in Kentucky reported the results shown in the table. (Data from T. Keil and G. Vito, Amer. J. Criminal Justice , vol. 20, 1995, pp. 17 €“ 36.)a. Find and compare the percentage of white defendants with the percentage of black defendants who received the death
The following list summarizes shooting percentage in the 2001–2002 season in the National Basketball Association by Brent Barry and Shaquille O’Neal. 2-point shots • Brent Barry: 58.8% (237/403) • Shaquille O’Neal: 58.0% (712/1228) 3-point shots • Brent Barry: 42.4% (164/387) •
The American Association of University Professors (AAUP) reports yearly on faculty salaries for all types of higher education institutions across the United States. The following table lists the mean salary, in thousands of dollars, of full-time instructional faculty on nine-month contracts at
The table shows the mean number of children in Canadian families, classified by whether the family was English speaking or French speaking and by whether the family lived in Quebec or in another province.a. Overall, compare the mean number of children for English-speaking and French-speaking
In the United States, the median age of residents is lowest in Utah. At each age level, the death rate from heart disease is higher in Utah than in Colorado. Overall, the death rate from heart disease is lower in Utah than Colorado. Are there any contradictions here, or is this possible? Explain.
The percentage of women who get breast cancer sometime during their lifetime is higher now than in 1900. Suppose that breast cancer incidence tends to increase with age, and suppose that women tend to live longer now than in 1900. Explain why a comparison of breast cancer rates now with the rate in
Refer to the previous exercise. a. State the hypotheses that were tested. b. Explain how to interpret the P-value for the test. c. Report the P-value for the one-sided alternative hypothesis that the chance of death due to heart attack is lower for the aspirin group. d. Even though the difference
Steve Solomon, the owner of Leonardo’s Italian restaurant, wonders whether a redesigned menu will increase, on the average, the amount that customers spend in the restaurant. For the following scenarios, pick a statistical method from this chapter that would be appropriate for analyzing the data,
A report (December 4, 2002) by the Pew Research Center on What the World Thinks in 2002 reported that, “The American public is strikingly at odds with publics around the world in its views about the U.S. role in the world and the global impact of American actions.” Conclusions were based on
The Centers for Disease Control (www.cdc.gov) periodically takes large randomized surveys to track health of Americans. In a survey of 11,207 adults in 1976–1980, 47% were overweight (body mass index BMI Ú 25). In a survey of 4431 adults in 2003–2004, 66% were overweight. a. Estimate the
In a survey conducted by Wright State University, senior high school students were asked if they had ever used marijuana. The table shows results of one analysis, where X is the count who said yes. Assuming these observations can be treated as a random sample from a population of interest,a.
The table shows results from the 2008 General Social Survey on gender and whether or not one believes in an afterlife.a. Denote the population proportion who believe in an afterlife by p1 for females and by p2 for males. Estimate p1, p2, and (p1 - p2).b. Find the standard error for the estimate of
Refer to the previous exercise. a. Find the standard error of (p̂1 – p̂2) for a test of H0: p1 = p2. b. For a two-sided test, find the test statistic and P-value, and make a decision using significance level 0.05. Interpret. c. Suppose that actually p1 = 0.81 and p2 = 0.72. Was the decision in
A recent GSS reported that the 486 surveyed females had a mean of 8.3 close friends (s = 15.6) and the 354 surveyed males had a mean of 8.9 close friends (s = 15.5). a. Estimate the difference between the population means for males and females. b. The 95% confidence interval for the difference
A study of a sample of horseshoe crabs on a Florida island (J. Brockmann, Ethology , vol. 102, 1996, pp. 1€“21) investigated the factors that were associated with whether or not female crabs had a male crab mate. Basic statistics, including the five-number summary on weight (kg) for the 111
The 2008 GSS asked about the number of hours you watch TV per day. An analysis that evaluates this by race shows the results (note the codes: 1 = Black and 2 = White):T-Test of difference = 0 (vs not =): T-Value = 5.96 P-Value = 0.000 a. Do you believe that TV watching has a normal distribution for
Refer to the previous exercise. a. Specify the hypotheses that are tested in the output shown. b. Report the value of the test statistic and the P-value Interpret. c. Make a decision, using the 0.05 significance level. d. Explain the connection between the result of this significance test in part c
In the study for cancer death rates, consider the null hypothesis that the population proportion of cancer deaths p1 for placebo is the same as the population proportion p2 for aspirin. The sample proportions were p̂1 = 347/11,535 = 0.030 and p̂2 = 327/14,035 = 0.023. a. For testing H0: p1 = p2
When the General Social Survey last asked the number of hours the respondent spent a week on housework (variable RHHWORK), the responses were summarized for females and males bya. Identify the response variable and explanatory variable. Indicate whether each is quantitative or categorical. b. A 95%
In 2006, the General Social Survey asked about the number of hours a week spent on the World Wide Web (variable denoted WWWTIME). Some results are as follows:a. Identify the response variable and explanatory variable. Indicate whether each variable is quantitative or categorical. b. Report and
In the previous exercise, explain how the result of the 99% confidence interval in part b corresponds to the result of the decision using significance level 0.01 in part c.
A study of the effect of the gender of the tester on sex-role differentiation scores 16 in Manhattan gave a random sample of preschool children the Occupational Preference Test. Children were asked to give three choices of what they wanted to be when they grew up. Each occupation was rated on a
A recent General Social Survey asked, €œHow many days in the past seven days have you felt sad?€ Software comparing results for men and women who responded showed the following results.T-Test of difference = 0 (vs not =): T-Value = 4.84 P-Value = 0.000 a. Explain how to
A recent study interviewed youths with a battery of questions that provides a summary measure of perceived parental support. This measure had sample means of 46 (s = 9) for the single-mother households and 42 (s = 10) for the households with both biological parents. One conclusion in the study
Automobile company compares two different types of front bumpers for their new model by driving sample cars into a concrete wall at 20miles per hour. The response is the amount of damage to the car, as measured by the repair costs, in hundreds of dollars. Due to the costs, the study uses only six
Example 8 in Section 9.3 described a study that used a cognitive behavioral therapy to treat a sample of teenage girls who suffered from anorexia. The study observed the mean weight change after a period of treatment. Studies of that type also usually have a control group that receives no treatment
Refer to the previous exercise. For the control group, the 26 changes in weights have a mean of -0.45. From Example 8 in Chapter 9, for the therapy group the sample mean change in weight of 3.0 pounds was significantly different from 0. However, the previous exercise showed it is not significantly
Refer to Example 10 on whether arthroscopic surgery is better than placebo. The following table shows the pain scores one year after surgery. Using software (such as MINITAB) that can conduct analyses using summary statistics, compare the placebo to the debridement group using a 95% confidence
In the study of binge drinking mentioned in Exercise 10.3, the percent who said they had engaged in unplanned sexual activities because of drinking alcohol was 30.7% in 1999 and 23.0% in 2009. Is this change statistically significant at the 0.05 significance level? a. Specify assumptions, notation,
Refer to the previous exercise. Compare the placebo to the debridement group using a significance test. State the assumptions, and explain how to interpret the P-value.
Refer to Exercise 10.87, comparing mean weight changes in anorexic girls for cognitive behavioral therapy and a control group. The MINITAB output shows results of doing analyses while assuming equal population standard deviations.MINITAB output for comparing mean weight changesT-Test of difference
A Danish study of individuals born at a Copenhagen hospital between 1959 and 1961 reported higher mean IQ scores for adults who were breast-fed for longer lengths of time as babies (E. Mortensen et al., JAMA, vol. 287, 2002, pp. 2365 – 2371). The mean IQ score was 98.1 (s = 15.9) for the 272
A study published by the National Cancer Institute (V. Kirsh et al., 2005) reported on the effect of lycopene and tomato product intake on the risk of prostate cancer. The study followed the health history and dietary habits of 29,361 men during an average of 4.2 years of follow-up over which time
A study followed patients for four years after they had a heart attack (K. Mukamal et al., Circulation, vol. 105, 2002, pp. 2476–2481). Patients were interviewed about their weekly caffeinated tea consumption during the year before the heart attack. The relative risk of another heart attack
The U.S. Department of Justice (www.ojp.usdoj.gov/bjs) gives incarceration rates in the nation’s prisons for various groups. a. In 2006, the incarceration rate was 1 per 109 male residents and 1 per 1563 female residents. Find the ratio of incarceration rates, and interpret. b. In 2006, the
In Western Australia, handheld cell phone use while driving has been banned since 2001, but hands-free devices are legal. A study (published in the British Medical Journal in 2005) of 456 drivers in Perth who had been in a crash that put them in a hospital emergency room observed if they were using
Each of a random sample of 10 customer service representatives from a large department store chain answers a questionnaire about how they respond to various customer complaints. Based on the responses, a summary score measures how positively the employees react to complaints. This is measured both
A tire manufacturer believes that a new tire it is introducing (Brand A) will have longer wear than the comparable tire (Brand B) sold by its main competitor. To get evidence to back up its claim in planned advertising, the manufacturer conducts a study. On each of four cars it uses a tire of Brand
A study 17 compared personality characteristics between 49 children of alcoholics and a control group of 49 children of non-alcoholics who were matched on age and gender. On a measure of wellbeing, the 49 children of alcoholics had a mean of 26.1 (s = 7.2) and the 49 subjects in the control group
In the United States, is there a gender gap in political beliefs? That is, do women and men tend to differ in their political thinking and voting behavior? The table taken from the 2008 GSS relates gender and political party identification. Subjects indicated whether they identified more strongly
In Exercise 11.5 when you used the GSS to download a 3 Ã— 3 table for marital happiness and family income in 2008, you should have obtained results similar to the table shown below.a. State the null and alternative hypotheses for the test.b. How large a X2 value would give a P-value of exactly
In the 2008 GSS, 620 of 809 males and 835 of 978 females indicated a belief in life after death. a. Construct a 2 × 2 contingency table relating gender of respondent (SEX, categories male and female) as the rows to belief about life after death (POSTLIFE, categories yes and no) as the columns. b.
In pro basketball games during 1980–1982, when Larry Bird of the Boston Celtics missed his first free throw, 48 out of 53 times he made the second one, and when he made his first free throw, 251 out of 285 times he made the second one. a. Form a 2 × 2 contingency table that cross-tabulates the
The table on the following page refers to a survey 3 in which senior high school students in Dayton, Ohio, were randomly sampled. It cross-tabulates whether a student had ever smoked cigarettes and whether a student had ever used marijuana. Analyze these data by(a) Finding and interpreting
Refer to the previous exercise. A similar table relates cigarette use to alcohol use. The MINITAB output for the chi-squared test follows.a. True or false: If we use cigarette use as the column variable instead of alcohol use, then we will get different values for the chi-squared statistic and the
In 2000 the GSS asked whether a subject is willing to accept cuts in the standard of living to help the environment (GRNSOL), with categories (vw = very willing, fw = fairly willing, nwu = neither willing nor unwilling, nvw = not very willing, nw = not at all willing). When this was cross-tabulated
A Swedish study used 1360 patients who had suffered a stroke. The study randomly assigned each subject to an aspirin treatment or a placebo treatment. In this study heart attacks were suffered by 28 of the 684 subjects taking placebo and 18 of the 676 subjects taking aspirin. a. Report the data in
Refer to the previous exercise. The printout from MINITAB reports Test for difference = 0 (vs not = 0): Z = 1.46 P-Value = 0.144 a. Define population proportions p1 and p2 and state the hypotheses for that test. b. Explain how the result of the chi-squared test in (b) in the previous exercise
Are people who believe in life after death happier? a. Go to the GSS Web site sda.berkeley.edu/GSS and download the contingency table for the 2008 survey relating happiness and whether you believe in life after death (variables denoted HAPPY and POSTLIFE). Construct the conditional distributions,
Every year, a large-scale poll of college freshmen conducted by the Higher Education Research Institute at UCLA asks their opinions about a variety of issues. In 2004, although women were more likely to rate their time management skills as “above average,” they were also twice as likely as men
In an experiment on chlorophyll inheritance in corn, for 1103 seedlings of self-fertilized heterozygous green plants, 854 seedlings were green and 249 were yellow. Theory predicts that 75% of the seedlings would be green. a. Specify a null hypothesis for testing the theory. b. Find the value of the
Karl Pearson devised the chi-squared goodness-of-fit test partly to analyze data from an experiment to analyze whether a particular roulette wheel in Monte Carlo was fair, in the sense that each outcome was equally likely in a spin of the wheel. For a given European roulette wheel with 37 pockets
The table shows 2008 GSS data on race and political party identification.a. The chi-squared test of independence has X2 = 177.312. Carry out the five steps of the test, and interpret the result in the context of these variables. b. Estimate the difference between black subjects and white subjects
Refer to the previous exercise and to the data in the table below from Exercise 11.1. Which has a stronger association with whether one identifies as a Democrat€”race or gender? Justify your answer by comparing the difference between blacks and whites in the proportion identifying as
The table shows 2008 GSS data on happiness and the highest degree attained.a. The chi-squared test of independence has X2 = 64.41. What conclusion would you make using a significance level of 0.05? Interpret.b. Does this large chi-squared value mean there is a strong association between happiness
The table shows 2008 GSS data on family income and the subject€™s highest degree attained, for which X2 = 315.98 (P-value = 0.000).a. Estimate the difference between the lowest and highest education groups in the proportion who report (i) below average income and (ii) above average
The table refers to a survey4 of senior high school students in Dayton, Ohio. It cross-tabulates whether a student had ever smoked cigarettes and whether a student had ever drunk alcohol. The table also shows MINITAB output of conditional distributions.a. Describe the strength of association using
For murders in the United States in 2009, the table cross-tabulates the sex of the victim by the sex of the offender. Find and interpret a measure of association, treating sex of victim as the response variable.
According to the U.S. Department of Justice, in 2009 the incarceration rate in the nation’s prisons was 949 per 100,000 male residents, and 67 per 100,000 female residents. a. Find the relative risk of being incarcerated, comparing males to females. Interpret. b. Find the difference of
Data posted at the University of Georgia Web site indicated that of all female students in 2011, 78% were undergraduates, and of male students in 2011, 16% were graduate students. Let x denote gender of student and y denote type of student. a. Which conditional distributions do these statistics
According to summarized data from 1999 to 2006 accessed from the Centers of Disease Control and Prevention, the annual probability that a male teenager at age 19 is likely to die is about 0.00135 and 0.00046 for females age 19. (www.cdc.gov) a. Compare these rates using the difference of
Table 11.11, summarized again here, showed the associations between death penalty opinion and gender and race.a. True or false: The table with the larger X2 statistic necessarily has the stronger association. Explain. b. To make an inference about the strength of association in the population, you
The table displays the observed and expected cell counts and the standardized residuals for testing independence of happiness and family income, for GSS data.a. How would you interpret the standardized residual of 4.681? b. Interpret the standardized residuals highlighted in green. c. Interpret the
The table shows MINITAB output for data from the 2008 GSS on happiness and frequency of attending religious services (1 = at most several times a year, 2 = once a month to nearly every week, 3 = every week to several times a week).a. Based on the chi-squared statistic and P-value, give a conclusion
Table 11.15 showed the association between general happiness and marital happiness. The table shown here gives the standardized residuals for those data, in parentheses.a. Explain what a relatively small standardized residual such as -0.1 in the second cell represents.b. Identify the cells in which
For the 2008 GSS, the table shows cell counts and standardized residuals (in parentheses) for happiness and marital status. Summarize the association by indicating which marital statuses have strong evidence of(i) More and(ii) Fewer people in the population in the Very Happy category than if the
The table in Exercise 11.1 on gender and party identification is shown again. The largest standardized residuals in absolute value were 2.69 for females who identified as Democrats and -2.69 for males who identified as Democrats. Interpret.
Go to the GSS Web site sda.berkeley.edu/GSS/. For the 2008 survey, construct the 7 × 8 contingency table relating political ideology (POLVIEWS) and party identification (PARTYID). a. Summarize the results of carrying out the chi-squared test. b. Find the standardized residuals (by checking Show z
In an experiment with beagles ages 7–11, the dogs attempted to learn how to find a treat under a certain black-colored block and then relearn that task with a white-colored block. The control group of dogs received standard care and diet. The diet and exercise group were given dog food fortified
The contingency table shown relates happiness and gender for the 2008 GSS.a. Identify the response variable and the explanatory variable.b. Construct a table or graph showing the conditional distributions. Interpret.c. Give an example of population conditional distributions that would seem to be
Consider the tea-tasting experiment of Example 10 and Table 11.18. Consider the possible sample table in which all four of her predictions about the cups that had milk poured first are correct. Using software, find the P-value for the one-sided alternative. Interpret the P-value.Table 11.18
An advertisement by Schering Corporation for the allergy drug Claritin mentioned that in a pediatric randomized clinical trial, symptoms of nervousness were shown by 4 of 188 patients on Claritin and 2 of 262 patients taking placebo. Denote the population proportion who would show such symptoms by
Chatterjee et al. (1995, p. 132) described a study about the effect of condoms in reducing the spread of AIDS. This two-year Italian study followed heterosexual couples where one partner was infected with the HIV virus. Of 171 couples who always used condoms, 3 partners became infected with HIV,
When recent General Social Surveys have asked, “If your party nominated a woman for president, would you vote for her if she were qualified for the job?” about 94% of females and 94% of males answered yes, the rest answered no. a. For males and for females, report the conditional distributions
The table shown, from Example 8 in Chapter 5, cross-tabulates whether a fetus has Down syndrome by whether or not the triple blood diagnostic test for Down syndrome is positive (that is, indicates that the fetus has Down syndrome).a. Tabulate the conditional distributions for the blood test result,
For the data in the previous exercise, X2 = 114.4. Show all steps of the chi-squared test of independence.Previous exercise data
The contingency table that follows has df = 4. Show this, by filling in the missing cell counts.
A recent randomized experiment of a multi-herbal formula (Immumax) containing echinacea, garlic, ginseng, zinc and vitamin C, was found to improve cold symptoms in adults over a placebo group. “At the end of the study, eight (39%) of the placebo recipients and 18 (60%) of the Immumax recipients
The table shows GSS data on happiness and the number of close friends, with expected cell counts given underneath the observed counts.a. Suppose the variables were independent. Explain what this means in this context. b. Explain what is meant by an expected cell count. Show how to get the expected
Exercise 11.1 showed a 2 Ã— 3 table relating gender and political party identification, shown again here. The chi-squared statistic for these data equals 8.294. Conduct all five steps of the chi-squared test.
In the GSS, subjects who were married were asked about the happiness of their marriage, the variable coded as HAPMAR. a. Go to the GSS Web site sda.berkeley.edu/GSS/ and construct a contingency table for 2008 relating HAPMAR (the column variable) to family income as measured in this section, by
A recent GSS was used to cross-tabulate income ($40 thousand) in dollars with job satisfaction (very dissatisfied, little dissatisfied, moderately satisfied, very satisfied) for 96 subjects. a. For these data, X2 = 6.0. What is its df value, and what is its approximate sampling distribution, if H0
A study in the New England Journal of Medicine compared cardiovascular events for treatments of low-dose aspirin or placebo among 39, 876 healthy female health care providers for an average duration of about 10 years. Results indicated that women receiving aspirin and those receiving placebo did
A recent GSS presented the statement, “Women should take care of running their homes and leave running the country up to men,” and 14.8% of the male respondents agreed. Of the female respondents, 15.9% agreed. Of respondents having less than a high school education, 39.0% agreed. Of respondents
The table refers to passengers in autos and light trucks involved in accidents in the state of Maine in a recent year.a. Use the difference of proportions to describe the strength of association. Interpret.b. Use the relative risk to describe the strength of association. Interpret.
The table shows data from an SPSS printout for some analyses of 2008 GSS data on race and party ID.a. Interpret the expected count for the first cell.b. Interpret the standardized residual of 12.5 for the first cell (SPSS calls it an adjusted residual).c. How would you summarize to someone who has
A contingency table from the 2008 GSS relating happiness to number of sex partners in the previous year (0, 1, at least 2) had standardized residuals as shown in the table. Interpret the highlighted standardized residuals.Results on Happiness and Sex
When data from a recent GSS were used to form a 3 × 3 table that cross-tabulates highest degree (1 = less than high school, 2 = high school or junior college, 3 = bachelor or graduate) with religious beliefs (F = fundamentalist, M = moderate, L = liberal), the three largest standardized residuals
From a study described in Example 5 in the previous chapter, the proportion of males committing aggressive acts was 4 out of 45 for those who watched less than 1 hour of TV a day, and 117 out of 315 for those who watched at least 1 hour per day. MINITAB reports the printout shown for conducting
An advertisement for Botox Cosmetic by Allergan, Inc. for treating wrinkles appeared in several magazines. The back page of the ad showed the results of a randomized clinical trial to compare 405 people receiving Botox injections to 130 people receiving placebo in terms of the frequency of various
Refer to the FL Student Survey data file on the text CD. Using software, create and analyze descriptively and inferentially the contingency table relating religiosity and belief in life after death. Summarize your analyses in a short report.
Which one of the following variables would you think most likely to be independent of happiness: belief in an afterlife, family income, quality of health, region of the country in which you live, satisfaction with job? Explain the basis of your reasoning.
At sda.berkeley.edu/GSS, cross-tabulate HAPMAR with YEAR, so you can see how conditional distributions on marital happiness in the GSS have changed since 1973. Using conditional distributions and standardized residuals, explain how these results show a very slight trend over time for fewer people
A young child wonders what causes women to have babies. For each woman who lives on her block, she observes whether her hair is gray and whether she has young children, with the results shown in the table that follows.a. Construct the 2 Ã— 2 contingency table that cross-tabulates gray
According to recent United Nations figures, the annual gun homicide rate is 62.4 per one million residents in the United States and 1.3 per one million residents in Britain. a. Show how to compare the proportion of residents of the two countries killed annually by guns using the difference of
The State Center for Health Statistics for the North Carolina Division of Public Health released a report in 2010 that indicates that there are racial disparities in colorectal cancer incidence and mortality rates. The report states, “African Americans are less likely to receive appropriate
Refer to the previous exercise. Go to the GSS Web site and construct a table relating happiness (HAPPY) to the variable you chose (AFTERLIF, FINRELA, HEALTH, REGION, or JOBSAT). Inspect the conditional distributions and indicate whether independence seems plausible, with the sample conditional
In any significance test, when the sample size is very large, we have not necessarily established an important result when we obtain statistical significance. Explain what this means in the context of analyzing contingency tables with a chi-squared test.
When df = 1, the P-value from the chi-squared test of independence is the same as the P-value for the two-sided test comparing two proportions with the z test statistic. This is because of a direct connection between the standard normal distribution and the chi-squared distribution with df = 1:

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