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

The authorship of an old document is in doubt. A historian hypothesizes that the author was a journalist named Jacalyn Levine. Upon a thorough investigation of Levine’s known works, it is observed that one unusual feature of her writing was that she consistently began 10% of her sentences with
For a quantitative variable, you want to test H0: μ = 0 against Ha: μ ≠ 0. The 10 observations are 3, 7, 3, 3, 0, 8, 1, 12, 5, 8. a. Show that (i) x = 5.0, (ii) s = 3.71, (iii) Standard error = 1.17, (iv) Test statistic = 4.26, and (v) df = 9. b. The P-value is 0.002. Make a decision using a
Is the ideal number of children equal to 2, or higher or lower than that? For testing that the mean response from a recent GSS equals 2.0 for the question, €œWhat do you think is the ideal number of children to have?€ software shows results:a. Report the test statistic value,
When all subjects in the 2008 GSS who were working full- or part-time were asked how many hours they worked in the previous week at all jobs (variable HRS1), software produced the following analyses:For this printout, a. State the hypotheses. b. Explain how to interpret the values of (i) SE Mean,
Example 11 compared mean political beliefs (on a 1 to 7 point scale) to the moderate value of 4.0, using GSS data. Test whether the population mean equals 4.00 for females, for whom the sample mean was 3.98 and standard deviation was 1.45 for a sample of size 819. Carry out the five steps of a
When Vincenzo Baranello’s blood pressure is in control, his systolic blood pressure reading has a mean of 130. For the last six times he has monitored his blood pressure, he has obtained the values 140, 150, 155, 155, 160, 140. a. Does this provide strong evidence that his true mean has changed?
When it is operating correctly, a machine for manufacturing tennis balls produces balls with a mean weight of 57.6 grams. The last eight balls manufactured had weights 57.3, 57.4, 57.2, 57.5, 57.4, 57.1, 57.3, 57.0 a. Using a calculator or software, find the test statistic and P-value for a test of
A company that sells products through mail-order catalogs wants to evaluate whether the mean sales for their most recent catalog were different from the mean of $15 from past catalogs. For a random sample of 100 customers, the mean sales were $10, with a standard deviation of $10. Find a P-value to
Management claims that the mean income for all senior-level assembly-line workers in a large company equals $500 per week. An employee decides to test this claim, believing that it is actually less than $500. For a random sample of nine employees, the incomes are 430, 450, 450, 440, 460, 420, 430,
Refer to the previous exercise. a. For which significance levels can you reject H0? (i) 0.10, (ii) 0.05, or (iii) 0.01. b. Based on the answers in part a, for which confidence levels would the confidence interval contain 500? (i) 0.90, (ii) 0.95, or (iii) 0.99. c. Use part a and part b to
The P-value for testing H0: μ = 100 against Ha: μ ≠ 100 is 0.043. a. What decision is made using a 0.05 significance level? b. If the decision in part a is in error, what type of error is it? c. Does a 95% confidence interval for μ contain 100? Explain.
A person who claims to be psychic says that the probability p that he can correctly predict the outcome of the roll of a die in another room is greater than 1/6, the value that applies with random guessing. If we want to test this claim, we could use the data from an experiment in which he predicts
A journal article that deals with changes in religious beliefs over time states, “For these subjects, the difference in their responses on the scale of religiosity between age 16 and the current survey was statistically significant (P-value 6 0.05).” a. How would you explain to someone who has
In making a decision in a significance test, a researcher worries about rejecting H0 when it may actually be true. a. Explain how the researcher can control the probability of this type of error. b. Why should the researcher probably not set this probability equal to 0.00001?
Consider the analogy discussed in Section 9.4 between making a decision about a null hypothesis in a significance test and making a decision about the innocence or guilt of a defendant in a criminal trial. a. Explain the difference between Type I and Type II errors in the trial setting. b. In this
Consider Example 13 about testing H0: p = 1/3 against Ha: p > 1/3 for the astrology study, with n = 116. Find P(Type II error) for testing H0: p = 1/3 against Ha: p > 1/3 when actually p = 0.50, if the sample size is 60 instead of 116. Do this by showing that a. The standard error is 0.061 when H0
Refer to the FL Student Survey data file on the text CD. Test whether the (a) Population mean political ideology (on a scale of 1 to 7, where 4 = moderate) equals or differs from 4.0. (b) Population proportion favoring affirmative action equals or differs from 0.50. For each part, write a one-page
A GSS question asked the gender of your best friend. Of 1381 people interviewed, 147 said their best friend had the opposite gender, and 1234 said their best friend had the same gender. Prepare a short report in which you analyze these data using a confidence interval and a significance test. Which
In major league baseball’s 2010 season, the home team won 1359 games and the away team won 1071 (www.mlb.com). a. Although these games are not a random sample, explain how you could think of these data as giving you information about some long-run phenomenon. b. Analyze these data using (i) a
The president of the American Statistical Association stated, “Statistics has become the modern-day enforcer of scientific objectivity. Terms like randomization, blinding, and 0.05 significance wield a no-doubt effective objectivity nightstick.” He also discussed how learning what effects
A medical researcher gets a P-value of 0.056 for testing H0: μ = 0 against Ha: μ ≠ 0. Since he believes that the true mean is positive and is worried that his favorite journal will not publish the results because they are not “significant at the 0.05 level,” he instead reports in his
According to the Bureau of Labor Statistics, the official unemployment rate was 15.5% among Blacks and 7.9% among Whites as of March 2011. During the recession of 2009–2011, the Black levels of unemployment have been similar or in many locations higher than those during the Great Depression era
Two TV commercials are developed for marketing a new product. A volunteer test sample of 200 people is randomly split into two groups of 100 each. In a controlled setting, Group A watches commercial A and Group B watches commercial B. In Group A, 25 say they would buy the product. In group B, 20
Consider the results from the previous exercise. a. Construct a 95% confidence interval to compare the population means. b. Explain what you learn from the confidence interval that you do not learn from the significance test.
A researcher in the College of Nursing, University of Florida, hypothesized that women who undergo breast augmentation surgery would gain an increase in self-esteem. The article about the study 18 indicated that for the 84 subjects who volunteered for the study, the scores on the Rosenberg
As part of her class project in a statistics course, a student decided to study ways in which her fellow students use the Internet. She randomly sampled 5 of the 165 students in her course and asked them, €œIn the past week, how many days did you use the Internet to (a) Read news stories.
In a recent General Social Survey, subjects were asked to respond to the following: €œChildren are exposed to many influences in their daily lives. What kind of influence does each of the following have on children? 1. Programs on network television, 2. rock music.€ The
Refer to the previous exercise. The GSS also asked about the influence of movies. The responses for these 12 subjects were -1, 1, 0, 2, 0,-2, -1, 0,-1, 1, 1, -1. The results of using MINITAB to compare the influence of movies and TV are shown below. Explain how to interpret(a) The confidence
The table summarizes results of a crossover study to compare results of low-dose and high-dose analgesics for relief of menstrual bleeding (B. Jones and M. Kenward, Statistics in Medicine, vol. 6, 1987, pp. 555€“564).a. Find the sample proportion of successes for each dose of the
A poll by Louis Harris and Associates of 1249 Americans indicated that 36% believe in ghosts and 37% believe in astrology. a. Is it valid to compare the proportions using inferential methods for independent samples? Explain. b. Do you have enough information to compare the proportions using methods
A March 2003 article in the Gainesville Sun about a study at Boston’s Children’s Hospital had the headline, “New study: Lots of fast food and TV triple risk of obesity.” The response variable was binary, namely whether a child was obese. Define, in terms of this study, the sample statistic
For automobile accidents in a recent year in Maine, injuries occurred to 3865 of 30,902 subjects not wearing seat belts, and to 2409 of 37,792 subjects wearing seat belts. Find and interpret the relative risk for these data.
Exercise 3.58 showed results of another study about the death penalty and race. The data are repeated here.a. Treating victim€™s race as the control variable, show that Simpson€™s paradox occurs.b. Explain what causes the paradox to happen.
The Women’s Health Initiative conducted a randomized experiment to see if hormone therapy was helpful for postmenopausal women. The women were randomly assigned to receive the estrogen plus progestin hormone therapy or a placebo. After five years, 107 of the 8506 on the hormone therapy developed
The crude death rate is the number of deaths in a year, per size of the population, multiplied by 1000. a. According to the U.S. Bureau of the Census, in 1995 Mexico had a crude death rate of 4.6 (i.e., 4.6 deaths per 1000 population) while the United States had a crude death rate of 8.4. Explain
For a particular Big Ten university, the mean income for male faculty is $8000 higher than the mean income for female faculty. Explain how this difference could disappear: a. Controlling for number of years since received highest degree. (What if relatively few female professors were hired until
Refer to the FL Student Survey data file on the text CD. Using software, prepare a short report summarizing the use of confidence intervals and significance tests (including checking assumptions) to compare males and females in terms of opinions about whether there is life after death.
The results in the table are from a study of physical attractiveness and subjective well-being (E. Diener et al., Journal of Personality and Social Psychology, vol. 69, 1995, pp. 120€“129). As part of the study, college students in a sample were rated by a panel on their physical
A Time Magazine article titled “Wal-Mart’s Gender Gap” (July 5, 2004) stated that in 2001 women managers at Wal-Mart earned $14,500 less than their male counterparts. a. If these data are based on a random sample of managers at Wal-Mart, what more would you need to know about the sample to
Two new programs were recently proposed at the University of Florida for treating students who suffer from math anxiety. Program A provides counseling sessions, one session a week for six weeks. Program B supplements the counseling sessions with short quizzes that are designed to improve student
An AP story (April 9, 2005) with headline Study: Attractive People Make More stated that “A study concerning weight showed that women who were obese earned 17 percent lower wages than women of average weight.” a. Identify the two variables stated to have an association. b. Identify a control
A researcher predicts that the percentage of people who do not watch TV is higher now than before the advent of the Internet. Let p1 denote the population proportion of American adults in 1975 who reported watching no TV. Let p2 denote the corresponding population proportion in 2008. a. Set up null
A test consists of 100 true-false questions. Joe did not study, and on each question he randomly guesses the correct response. Jane studied a little and has a 0.60 chance of a correct response for each question. a. Approximate the probability that Jane’s score is nonetheless lower that
From the box formula for the standard error at the end of Section 10.1,se(estimate 1 - estimate 2) =√[se(estimate 1)]2 + [se(estimate 2)]2,if you know the se for each of two independent estimates, you can find the se of their difference. This is useful, because often articles report a se for each
a. For comparisons of groups in which n1 = n2, with common value denoted by n , use the fact that the largest possible value of p̂(1 - p̂) occurs at p̂ = 0.5 to show that the margin of error for a large-sample 95% confidence interval for (p1 - p2) can be no greater than 22√0.5/n = √22/n. b.
The small-sample confidence interval for comparing two proportions is a simple adjustment of the large-sample one. Recall that for a small-sample confidence interval for a single proportion, we used the ordinary formula after adding four observations; two of each type (see the end of Section 8.4).
The figure illustrates Simpson’s paradox for Example 17 on the death penalty. For each defendant’s race, the figure plots the percentage receiving the death penalty. Each percentage is labeled by a letter symbol giving the category of the victim’s race. Surrounding each observation is a
A February 2007 story on www.redandblack.com stated, “Students who use laptops in class have lower GPAs, according to a study by Cornell University.” a. Suppose this conclusion was based on a significance test comparing means. Defining notation in context, identify the groups and the population
You would like to determine what students at your school would be willing to do to help address global warming and the development of alternatively fueled vehicles. To do this, you take a random sample of 100 students. One question you ask them is, “How high of a tax would you be willing to add
Do women tend to spend more time on housework than men? If so, how much more? Based on data from the National Survey of Families and Households, one study reported the results in the table for the number of hours spent in housework per week. (Source: Data from A. Lincoln, Journal of Marriage and
Refer to part c in the previous exercise. Calculate the 95% confidence interval comparing the population means for women and men. Interpret the result including the relevance of 0 being within the interval or not. a. Show that a 99% confidence interval is (10.0, 16.2). (For such large sample sizes,
The study described in Exercise 10.16 also evaluated the weekly time spent in employment. This sample comprises men and women with a high level of labor force attachment. Software shows the results.a. Does it seem plausible that employment has a normal distribution for each gender? Explain. b. What
The Web site sda.berkeley.edu/GSS for the General Social Survey enables you to compare means for groups. Compare female and male responses on the question, “What is the ideal number of children for a family to have?” in 2008. Identify CHLDIDEL as the dependent variable, SEX as the row variable,
The 2009 Sleep in America poll of a random sample of 1000 adults reported that respondents slept an average of 6.7 hours on weekdays and 7.1 hours on weekends, and that 28% of respondents got eight or more hours of sleep on weekdays whereas 44% got eight or more hours of sleep on weekends
The study described in the Exercise 10.18 also evaluated personal income by gender. The average earnings per year were $35,800 for men with a standard deviation of $14,600. The average earnings for women were $23,900 with a standard deviation of $21,900. Software shows the following results:a. Does
A study of bulimia among college women (J. Kern and T. Hastings, Journal of Clinical Psychology, vol. 51, 1995, p. 499) studied the connection between childhood sexual abuse and a measure of family cohesion (the higher the score, the greater the cohesion). The sample mean on the family cohesion
Chelation is an alternative therapy for heart disease that uses repeated intravenous administration of a human-made amino acid in combination with oral vitamins and minerals. Practitioners believe it removes calcium deposits from buildup in arteries. However, the evidence for a positive effect is
Refer to Examples 6€“8 on nicotine dependence for teenage smokers. Another explanatory variable was whether a subject reported inhaling when smoking. The table reports descriptive statistics.a. Explain why (i) the overwhelming majority of noninhalers must have had HONC scores of 0 and
Refer to the previous exercise. a. Show that the test statistic for H0: μ1 = μ2 equals t = 11.7. If the population means were equal, explain why it would be nearly impossible by random variation to observe this large a test statistic. b. What decision would you make about H0, at common
Refer to Example 6, “Teenagers on Nicotine.” Of those who had tried tobacco, the mean HONC score was 2.8 (s = 3.6) for the 150 females and 1.6 (s = 2.9) for the 182 males.a. Find a standard error for comparing the sample means. Interpret.b. Find the test statistic and P-value for H0: μ1 = μ2
Refer to the previous exercise. A subject was called a monthly smoker if he or she had smoked cigarettes over an extended period of time. The 74 female monthly smokers had a mean HONC score of 5.4 (s = 3.5), and the 71 male monthly smokers had a mean HONC score of 3.9 (s = 3.6). Using software
For the 2008 General Social Survey, a comparison of females and males on the number of hours a day that the subject watched TV gavea. Set up the hypotheses of a significance test to analyze whether the population means differ for females and males. b. Using software (such as MINITAB) in which you
Refer to the FL Student Survey data file on the text CD. Use the number of times reading a newspaper as the response variable and gender as the explanatory variable. The observations are as follows:Using software, a. Construct and interpret a plot comparing responses by females and males. b.
A graduate teaching assistant for Introduction to Statistics (STA 2023) at the University of Florida collected data from students in one of her classes in spring 2007 to investigate whether study time per week (average number of hours) differed between students in the class who planned to go to
The PACE project (pace.uhs.wisc.edu) at the University of Wisconsin in Madison deals with problems associated with high-risk drinking on college campuses. Based on random samples, the study states that the percentage of UW students who reported bingeing at least three times within the past two
Refer to the data in the previous exercise.a. Show all steps of a two-sided significance test of the null hypothesis that the population mean is equal for the two groups. Interpret results in context.b. Based on the explanation given in the previous exercise, do you think that the sample was a
As part of a class exercise, an instructor at a major university asks her students how many hours per week they spend on social networks. She wants to investigate if time spent on social networks differs for male and female students at this university. The results for those age 21 or under were:a.
In the previous exercise, plot the data. Do you see any outliers that could influence the results? Remove the most extreme observation from each group and redo the analyses. Compare results and summarize the influence of the extreme observations
The methods of this section make the assumption of a normal population distribution. Why do you think this is more relevant for small samples than for large samples?
Female college student participation in athletics has increased dramatically over the past few decades. Sports medicine providers are aware of some unique health concerns of athletic women, including disordered eating. A study (M. Reinking and L. Alexander, Journal of Athletic Training, vol. 40,
Refer to the previous exercise. a. Find the P-value for testing whether the population means are equal. Use a two-sided alternative. b. Summarize assumptions for the analysis in part a. Do you think the normality assumption is justified? If not, what is the consequence of violating it?
Refer to Example 10, “Arthroscopic Surgery.” Here we show MINITAB output comparing mean knee pain scores for the placebo (Group 1) to debridement arthroscopic surgery (Group 2). a. State and interpret the result of the confidence interval. b. State all steps and interpret the result of the
A clinical psychologist wants to choose between two therapies for treating severe cases of mental depression. She selects six patients who are similar in their depressive symptoms and in their overall quality of health. She randomly selects three of the patients to receive Therapy 1, and the other
Refer to the previous exercise.a. For the null hypothesis, H0: μ1 = μ2, show that t = 2.62 and the two-sided P-value = 0.059. Interpret.b. What decision would you make in the test, using a(i) 0.05 and(ii) 0.10 significance level?Explain what this means in the context of the study.c. Suppose the
When a sample of social science graduate students at the University of Florida gave their responses on political ideology (ranging from 1 = very liberal to 7 = very conservative), the mean was 3.18 (s = 1.72) for the 51 non-vegetarian students and 2.22 (s = 0.67) for the 9 vegetarian students.
The National Health Interview Survey conducted of 27,603 adults by the U.S. National Center for Health Statistics in 2009 indicated that 20.6% of adults were current smokers. A similar study conducted in 1991 of 42,000 adults indicated that 25.6% were current smokers. a. Find and interpret a point
One scientific €œtest of whiteness€ study mentioned in Example 1 tested the effect of a self applied tooth-whitening peroxide gel system in a randomized, controlled clinical trial. 11 The 58 adults assigned to the gel whitening group applied the gel after normal brushing
A study in Rotterdam (European Journal of Heart Failure, vol. 11, 2009, pp. 922–928) followed the health of 7983 subjects over 20 years to determine whether intake of fish could be associated with a decreased risk of heart failure in a general population of men and women aged 55 years and older.
For the Swedish study described in Exercise 10.6, during the follow-up period 28 of 684 taking placebo died from a heart attack and 18 of 676 taking aspirin died from a heart attack. a. Show that the relative risk for those taking placebo compared to those taking aspirin is 1.54. Interpret. b.
a. A New York Times health article (August 13, 2009) about a new study reported in the Journal of American Medical Association stated that, “patients with colorectal cancer who were regular aspirin users had a much better chance of surviving than nonusers, and were almost one third less likely to
Childhood obesity continues to be a leading public health concern that disproportionately affects low-income and minority children. According to the National Center for Health Statistics, obesity prevalence among low-income, preschool-aged children increased steadily from 12.4% in 1998 to 14.5% in
According to the U.S. Census, the median individual yearly income for whites in the United States was $33,808 in 1990, almost three times the median individual yearly income for Hispanics, which was $12,028 for that same year. In 2008, the median income for whites increased to $35,120 and for
Several recent studies have suggested that people who suffer from abnormally high blood pressure can benefit from regular exercise. A medical researcher decides to test her belief that walking briskly for at least half an hour a day has the effect of lowering blood pressure. She conducts a small
Refer to the previous exercise. The output shows some results of using software to analyze the data with a significance test.Paired T for Before€”AfterT-Test of mean difference = 0 (vs not = 0): T-Value = 6.93 P-Value = 0.020 a. State the hypotheses to which the reported P-value
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:
Let p1 and p2 denote the population proportions of males and females in the United States who answer, yes, definitely when asked whether they believe in miracles. Estimate these by going to the General Social Survey Web site (sda.berkeley.edu/GSS), selecting GSS with No Weight as the default weight
Refer to the previous exercise. The output shows the result of comparing the mean responses on parties and sports.Paired T for parties - sportsDifference 10 12.8000 22.5477 7.130295% CI for mean difference: (-3.3297, 28.9297)T-Test of mean difference = 0 (vs not = 0):T-Value = 1.80 P-Value =
Refer to the previous two exercises. Using software, compare the responses on movies and parties using (a) All steps of a significance test (b) A 95% confidence interval. Interpret results in context.
The freshman 15 is the name of a common belief that college students, particularly women, gain an average of 15 pounds during their first year of college. A recent study ( Journal of American Health , vol. 58, 2009, pp. 223–231) found that female students weighed an average of 133.0 pounds at the
Refer to the previous exercise. Suppose that the change in weight scores for the 132 freshmen had a standard deviation of 2.0 pounds.a. Explain how this standard deviation could be so much less than the standard deviation of 30 for the weight scores at each time.b. Is 15 pounds a plausible mean
Anna’s project for her introductory statistics course was to compare the selling prices of textbooks at two Internet bookstores. She first took a random sample of 10 textbooks used that term in courses at her college, based on the list of texts compiled by the college bookstore. The prices of
For the data in the previous exercise, use software or a calculator to perform a significance test comparing the population mean prices. Show all steps of the test, and indicate whether you would conclude that the mean price is lower at one of the two Internet bookstores.
Table 10.14 in Example 16, repeated here, showed results of an experiment comparing the results of two speech recognition systems, GMDS and CDHMM.a. Estimate the population proportion p1 of correct results for GMDS and p2 of correct results for CDHMM. b. Software reports a 95% interval for p1 - p2
The table that follows refers to a sample of juveniles convicted of a felony in Florida. Matched pairs were formed using criteria such as age and the number of prior offenses. For each pair, one subject was handled in the juvenile court and the other was transferred to the adult court. The response
Many medical studies have used a large sample of subjects from Framingham, Massachusetts who have been followed since 1948. A recent study (Annals of Internal Medicine , vol. 138, pp. 24€“32, 2003) gave the contingency table shown for weight at a baseline time and then 20 years later.a.
A study was conducted to see if an advertisement campaign would increase market share for Sanka instant decaffeinated coffee (R. Grover and V. Srinivasan, J. Marketing Research , vol. 24, 1987, pp. 139€“153). Subjects who use instant decaffeinated coffee were asked which brand they bought
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. 4 The table shows MINITAB output, where X is the number of deaths due to heart attack during a follow-up period of about 3 years. Sample 1 received
Last month a random sample of 1000 subjects was interviewed and asked whether they thought the president was doing a good job. This month the same subjects were asked this again. The results are: 450 said yes each time, 450 said no each time, 60 said yes on the first survey and no on the second
Results of polls about belief in heaven and hell depend strongly on question wording. For instance, a survey conducted by the International Social Science Program at National Opinion Research Center (NORC) asked Americans whether they “definitely believe in heaven” or “definitely believe in
A USA Today story (May 22, 2010) about the medical benefits of moderate drinking of alcohol stated that a major French study links those who drink moderately to a lower risk for cardiovascular disease but challenges the idea that moderate drinking is the cause. “Instead, the researchers say,

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