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Statistics The Exploration And Analysis Of Data 6th Edition John M Scheb, Jay Devore, Roxy Peck - Solutions
=+c. What happens if you predict efficiency for a car with a 300-horsepower engine? Why do you think this has occurred?d. Interpret r 2in the context of this problem.
=+b. Substituting x 5 100 gives 5 29.0. Give two different interpretations of this number.yˆyˆ
=+a. How would you interpret b 5 2.150?
=+13.4 A sample of small cars was selected, and the values of x 5 horsepower and y 5 fuel efficiency (mpg)were determined for each car. Fitting the simple linear regression model gave the estimated regression equation 5 44.0 2 .150x.
=+c. Approximately what proportion of infants whose Mn intake is 5 will have a serum Mn greater than 5? Less than 3.8?
=+b. What is the probability that an infant whose Mn intake is 4.0 will have serum Mn greater than 5?
=+a. What is the mean value of serum Mn when Mn intake is 4.0? When Mn intake is 4.5?
=+13.3 Data presented in the article “Manganese Intake and Serum Manganese Concentration of Human Milk-Fed and Formula-Fed Infants” (American Journal of Clinical Nutrition [1984]: 872–878) suggest that a simple linear regression model is reasonable for describing the relationship between y 5
=+c. What is the average change in flow rate when pressure drop decreases by 5 in.?
=+b. What is the true average change in flow rate associated with a 1-in. increase in pressure drop? Explain.
=+a. What is the true average flow rate for a pressure drop of 10 in.? A drop of 15 in.?
=+13.2 The flow rate in a device used for air quality measurement depends on the pressure drop x (inches of water)across the device’s filter. Suppose that for x values between 5 and 20, these two variables are related according to the simple linear regression model with true regression line y 5
=+f. Would you use the model to predict mean usage for a 500-sq-ft house? Why or why not? (Note: There are no small houses in the community in which this model is valid.)
=+e. What is the average change in usage associated with a 100-sq-ft increase in size?
=+d. What is the average change in usage associated with a 1-sq-ft increase in size?
=+c. What is the mean value of gas usage for houses with 2100 sq ft of space?
=+b. Graph the population regression line by first finding the point on the line corresponding to x 5 1000 and then the point corresponding to x 5 2000, and drawing a line through these points.
=+13.1 Let x be the size of a house (sq ft) and y be the amount of natural gas used (therms) during a specified period. Suppose that for a particular community, x and y are related according to the simple linear regression model with b 5 slope of population regression line 5 .017 a 5 y intercept
=+suggest that individuals’ abilities to make correct identification differ for the different brands of cola?Number of Correct Identifications Cola 0 1 2 3 or 4 Coca-Cola 13 23 24 19 Pepsi Cola 12 20 26 21 Royal Crown 18 28 19 14
=+12.47 ● The article “Identification of Cola Beverages”(Journal of Applied Psychology [1962]: 356–360) reported on an experiment in which each of 79 subjects was presented with glasses of cola in pairs and asked to identify which glass contained a specific brand of cola. The accompanying
=+Test the null hypothesis that the proportion of accident claims submitted by drivers of each astrological sign is consistent with the proportion of policyholders of each sign. Use the information on the distribution of policyholders from Part (a) to compute expected frequencies and then carry
=+Astrological Observed Number Sign in Sample Aquarius 85 Aries 83 Cancer 82 Capricorn 88 Gemini 83 Leo 83 Libra 83 Pisces 82 Sagittarius 81 Scorpio 85 Taurus 84 Virgo 81
=+c. Suppose that a random sample of 1000 accident claims submitted to this insurance company is selected and each claim classified according to the astrological sign of the driver. (The accompanying table is consistent with accident rates given in the article.)
=+b. Why do you think that the proportion of Capricorn policyholders is so much higher than would be expected if the proportions are the same for all astrological signs?
=+a. Assuming that it is reasonable to treat the policyholders of this particular insurance company as a random sample of insured drivers in Australia, are the observed data consistent with the hypothesis that the proportion of policyholders is the same for each of the 12 astrological signs?
=+study of insurance claims that resulted in the following data for male policyholders of a large insurance company.Astrological Number of Sign Policyholders Aquarius 35,666 Aries 37,926 Cancer 38,126 Capricorn 54,906 Gemini 37,179 Leo 37,354 Libra 37,910 Pisces 36,677 Sagittarius 34,175 Scorpio
=+12.46 ● Drivers born under the astrological sign of Capricorn are the worst drivers in Australia, according to an article that appeared in the Australian newspaper The Mercury (October 26, 1998). This statement was based on a
=+b. Test the relevant hypotheses using a significance level of .05.
=+a. Is this a test of homogeneity or a test of independence?
=+of offense. The data in the accompanying table are based on summary values given in the article “Profile of Jail Inmates” (USA Today, April 25, 1991). We would like to know whether male and female inmates differ with respect to type of offense.Gender Type of Crime Male Female Violent 117 66
=+12.45 ● Jail inmates can be classified into one of the following four categories according to the type of crime committed: violent crime, crime against property, drug offenses, and public-order offenses. Suppose that random samples of 500 male inmates and 500 female inmates are selected, and
=+30 subjects contributed when shown the picture of the smiling child, 14 of 30 contributed when shown the picture of an unsmiling child, 16 of 26 contributed when shown the verbal message, and 18 of 22 contributed when shown only the identification of the charity. What conclusions can be drawn
=+on Donation” (Journal of Applied Social Psychology[1979]: 426–431), experimenters went door-to-door with four types of displays: a picture of a smiling child, a picture of an unsmiling child, a verbal message, and an identification of the charity only. At each door, they would randomly
=+12.44 When charities solicit donations, they must know what approach will encourage people to donate. Would a picture of a needy child tug at the heartstrings and convince someone to contribute to the charity? As reported in the article “The Effect of Photographs of the Handicapped
=+States in which they lived. The resulting data are summarized in the accompanying table. Is there an association between response (agree, disagree) and region of residence?Use a 5 .01.Response Region Agree Disagree Northeast 130 59 West 146 42 Midwest 211 52 South 291 47
=+a random sample of 978 adults. Each individual in the sample was asked whether he or she agreed with the following statement: “Sometimes it is necessary to discipline a child with a good, hard spanking.” Respondents were also classified according to the region of the United
=+12.43 ● The article “Regional Differences in Attitudes Toward Corporal Punishment” (Journal of Marriage and Family [1994]: 314–324) presents data resulting from
=+about drinking?” Responses are summarized in the accompanying 3 3 2 table. Using a significance level of .05, carry out a test to determine whether there is an association between age of children and parental response.Age of Children Response Preteen Teen Very Effective 126 149 Somewhat
=+12.42 ● The authors of the article “A Survey of Parent Attitudes and Practices Regarding Underage Drinking”(Journal of Youth and Adolescence [1995]: 315–334) conducted a telephone survey of parents with preteen and teenage children. One of the questions asked was “How effective do you
=+Is there evidence of an association between position and role? Test the relevant hypotheses using a 5 .01. What assumptions about how the data were collected must be true for the chi-square test to be an appropriate way to analyze these data?
=+a chase (be the first one to charge the prey), or she could participate and join the chase after it has been initiated.Data from the article are summarized in the accompanying table.Role Initiate Participate Position Chase in Chase Center 28 48 Wing 66 41
=+of the line or on the wing (end of the line) as they advance toward their prey. In addition to position, the role of the lioness was also considered. A lioness could initiate
=+Alcohol Consumption (No. of Drinks)a1/Wk 1/Wk 2–4/Wk 5–6/Wk 1/Day Never Smoked 3577 1711 2430 1211 1910 Smoked in the Past 1595 1068 1999 1264 2683 Currently Smokes 524 289 470 296 849
=+12.41 ● The article “Cooperative Hunting in Lions: The Role of the Individual” (Behavioral Ecology and Sociobiology [1992]: 445–454) discusses the different roles taken by lionesses as they attack and capture prey. The authors were interested in the effect of the position in line as
=+b. Based on your conclusion in Part (a), is it reasonable to conclude that smoking causes an increase in the desire to do risky things? Explain.
=+a. Is there sufficient evidence to conclude that there is an association between smoking status and desire to do risky things? Test the relevant hypotheses using a 5 .05.
=+Assume that it is reasonable to regard the sample as a random sample of Mexican-American male adolescents.
=+Mexican-American Adolescents” (Journal of School Health [1998]: 376–379):Smoking Status Smoker Nonsmoker Likes Risky Things 45 46 Doesn’t Like Risky Things 36 153
=+12.40 ● Each boy in a sample of Mexican American males, age 10–18, was classified according to smoking status and response to a question asking whether he likes to do risky things. The following table is based on data given in the article “The Association Between Smoking and Unhealthy
=+c. Is the result of your test in Part (b) consistent with what you expected based on your answer to Part (a)? If not, explain why your initial impression based on the percentages may not have been accurate. What aspect of the data set factors into your explanation?
=+b. Test the hypothesis that smoking status and alcohol consumption are independent.
=+a. Calculate row percentages by dividing each observed count by the corresponding row total. Are the proportions falling in each of the alcohol consumption categories similar for the three smoking categories?
=+12.39 ● The following table is based on data reported in“Light-to-Moderate Alcohol Consumption and Risk of Stroke Among U.S. Male Physicians” (New England Journal of Medicine [1999]: 1557–1564). The table is based on 21,870 male physicians age 40–84 who are participating in the
=+Do these data support the theory that the homicide rate is not the same over the four seasons? Test the relevant hypotheses using a significance level of .05.Season Winter Spring Summer Fall 328 334 372 327
=+a relationship between weather and violent crime. The author of the article “Is There a Season for Homicide?”(Criminology [1988]: 287–296) classified 1361 homicides according to season, resulting in the accompanying data.
=+Do the data provide evidence that the proportion of students graduating from colleges and universities in California for these ethnic group categories differs from the respective proportions in the population for California? Test the appropriate hypotheses using a 5 .01.12.38 Criminologists
=+contained in the article titled “Crumbling Public School System a Threat to California’s Future (Investor’s Business Daily, November 12, 1999).Ethnic Group Number in Sample White 679 Black 51 Hispanic 77 Asian 190 Other 3
=+12.37 ● According to Census Bureau data, in 1998 the California population consisted of 50.7% whites, 6.6%blacks, 30.6% Hispanics, 10.8% Asians, and 1.3% other ethnic groups. Suppose that a random sample of 1000 students graduating from California colleges and universities in 1998 resulted in
=+race combination and whether or not the convicted murderer receive a death sentence for convicted murders in North Carolina during 1993 to 1997.
=+The table was based on a study of all homicide cases in North Carolina for the period 1993 to 1997 where it was possible that the person convicted of murder could receive the death penalty. Explain why it would not be necessary(or appropriate) to use a chi-square test to determine if there was an
=+12.36 ● The article “Victim’s Race Affects Killer’s Sentence, Study Finds” (New York Times, April 20, 2001)included the following information:Defendant’s Victim’s Death Death Race Race Penalty Penalty Not white White 33 251 White White 33 508 Not white Not white 29 587 White Not
=+12.35 ● Job satisfaction of professionals was examined in the article “Psychology of the Scientist: Work-Related Attitudes of U.S. Scientists” (Psychological Reports [1991]:443–450). Each person in a random sample of 778 teachers was classified according to a job satisfaction variable
=+a. Use the given percentages to construct a two-way table with rows corresponding to the six countries and columns corresponding to the categories “believe in fortune-tellers”and “don’t believe in fortune-tellers.” Enter the observed counts in the table. (Hint: The observed counts for
=+were based on random samples of size 200 from each of the six countries.Percentage Who Believe in Country Fortune-Tellers Great Britain 42 West Germany 32 East Germany 22 Slovenia 55 Ireland 27 Northern Ireland 33
=+12.34 ● The accompanying table appeared in the article“Europe’s Receptivity to New Religious Movements:Round Two” (Journal for the Scientific Study of Religion[1993]: 389–397). Suppose that the percentages in the table
=+12.33 ● Can people tell the difference between a female nose and a male nose? This important (?) research question was examined in the article “You Can Tell by the Nose: Judging Sex from an Isolated Facial Feature” (Perception [1995]: 969–973). Eight Caucasian males and eight Caucasian
=+Victim’s Attire on Adolescent Judgments of Date Rape”(Adolescence [1995]: 319–323) are given in the accompanying table. Is there evidence that the proportion who believe that the story described a rape differs for the three different photo groups? Test the relevant hypotheses using a 5
=+victim dressed conservatively, or no picture. Each student was asked whether the situation described in the story was one of rape. Data from the article “The Influence of
=+12.32 ● A story describing a date rape was read by 352 high school students. To investigate the effect of the victim’s clothing on subject’s judgment of the situation described, the story was accompanied by either a photograph of the victim dressed provocatively, a photo of the
=+Is it reasonable to use the chi-square test to determine whether there is an association between handgun purchase within the year prior to death and whether the death was a suicide? Justify your answer.
=+12.31 ● The article “Mortality Among Recent Purchasers of Handguns” (New England Journal of Medicine [1999]:1583–1589) examined the relationship between handgun purchases and cause of death. Suppose that a random sample of 4000 death records was examined and cause of death was noted for
=+Based on these data, can you conclude that there is an association between seat location and nausea? Test the relevant hypotheses using a 5 .05.
=+12.30 ● The article “Motion Sickness in Public Road Transport: The Effect of Driver, Route and Vehicle” (Ergonomics [1999]: 1646–1664) reported that seat position within a bus may have some effect on whether one experiences motion sickness. The accompanying table classifies each person
=+b. The author writes “women and men fell into each of the six workaholism types to a similar degree.” Does the outcome of the test you performed in Part (a) support this conclusion? Explain.
=+a. Test the hypothesis that gender and workaholism type are independent.
=+Work Enthusiasts 20 41 Workaholics 32 37 Enthusiastic Workaholics 34 46 Unengaged Workers 43 52 Relaxed Workers 24 27 Disenchanted Workers 37 30
=+12.29 ● ▼ Do women have different patterns of work behavior than men? The article “Workaholism in Organizations: Gender Differences” (Sex Roles: A Journal of Research [1999]: 333–346) attempts to answer this question.Each person in a random sample of 423 graduates of a business
=+Do the data provide convincing evidence of an association between city of residence and vehicle type? Use a significance level of .05. You may assume that it is reasonable to regard the sample as a random sample of Bay area residents.
=+given in the accompanying table (The Relationship of Vehicle Type Choice to Personality, Lifestyle, Attitudinal and Demographic Variables, Technical Report UCD-ITSRR02-06, DaimlerCrysler Corp., 2002).City Vehicle Pleasant North San Type Concord Hill Francisco Small 68 83 221 Compact 63 68 106
=+12.28 ● A survey was conducted in the San Francisco Bay area in which each participating individual was classified according to the type of vehicle used most often and city of residence. A subset of the resulting data are
=+data consistent with summary quantities appearing in the report, the following table classifies individuals in the sample according to age group and whether or not the individual was considered to be in good health. Use the given data to test the hypothesis that age group and whether or not an
=+More than 25 118 79 12.27 ● The report “Health Insurance Coverage of the Near Elderly” (Urban Institute, July 2000) includes information from a study of American adults. The sample used in the study was a random sample of those who participated in the National Survey of America’s
=+what population would it be reasonable to generalize this conclusion?Gender Days of Vacation Male Female None 51 42 1–5 21 25 6–10 67 79 11–15 111 94 16–20 71 70 21–25 82 58
=+12.26 ● The 2006 Expedia Vacation Deprivation Survey(Ipsos Insight, May 18, 2006) described the results of a poll of working adults in Canada. Each person in a random sample was classified according to gender and the number of vacation days he or she usually took each year.The resulting data
=+these data support the hypothesis that there is an association between gender and the age at which smoking began?Age When Gender Smoking Began Male Female,16 25 10 16–17 24 17 18–20 28 32$21 19 34
=+12.25 ● Data consistent with summary quantities given in a paper that appeared in the British Medical Journal(“Cigarette Tar Yields in Relation to Mortality from Lung Cancer in the Cancer Prevention Study II Prospective Cohort” [2004]: 72–79) are shown in the accompanying table. Suppose
=+year and the number of sweet drinks consumed? Assume that it is reasonable to regard the sample of children in this study as representative of 2- to 3-year-old children and then test the appropriate hypotheses using a .05 significance level.Number of Sweet Overweight?Drinks Consumed per Day Yes
=+12.24 ● The paper “Overweight Among Low-Income Preschool Children Associated with the Consumption of Sweet Drinks” (Pediatrics [2005]: 223–229) described a study of children who were underweight or normal weight at age 2. Children in the sample were classified according to the number of
=+12.23 ● The report described in the previous exercise also classified students according to region of residence and whether or not they had a credit card with a balance of more than $7000. Do these data support the conclusion that there is an association between region of residence and whether
=+At Least No One Credit Credit Region Card Cards Northeast 401 164 Midwest 162 36 South 408 115 West 104 23
=+12.22 ● The report “Undergraduate Students and Credit Cards in 2004” (Nellie Mae, May 2005) included information collected from individuals in a random sample of undergraduate students in the United States. Students were classified according to region of residence and whether or not they
=+Response 2005 2002 All of the time 132 180 Most of the time 337 528 Some of the time 554 396 Never 169 96
=+12.21 ● The survey described in the previous exercise also asked the following question: “Please tell me whether you trust the President to do the right thing all of the time, most of the time, some of the time, or never. Use the data in the given table and an appropriate hypothesis test to
=+in 2003, 2004, and 2005 are summarized in the given table. The samples for each year were independently selected and are considered to be representative of the population of undergraduate students in the year the survey was conducted. Is there evidence that the distribution of political
=+12.20 ● The Harvard University Institute of Politics surveys undergraduates across the United States annually.Responses to the question “When it comes to voting, do you consider yourself to be affiliated with the Democratic Party, the Republican Party, or are you Independent or unaffiliated
=+b. To what population would it be reasonable to generalize the conclusions of Part (a)? Explain.Current Hormone Use Conjugated Esterified Equine None Estrogen Estrogen Venous Thrombosis 372 86 121 No Venous Thrombosis 1439 515 289
=+a. Is there convincing evidence that the proportions falling in to each of the hormone use categories is not the same for women who have been diagnosed with venous thrombosis and those who have not?
=+from the study are given in the accompanying table (Journal of the American Medical Association [2004]: 1581–1587). The women in each of the two samples were selected at random from the patients at a large HMO in the state of Washington.
=+12.19 ● In a study to determine if hormone therapy increases risk of venous thrombosis in menopausal women, each person in a sample of 579 women who had been diagnosed with venous thrombosis was classified according to hormone use. Each woman in a sample of 2243 women who had not been
=+Response Some- Not Country Never Rarely times Often Sure Italy 600 140 140 90 30 Spain 540 160 140 70 90 France 400 250 200 120 30 United States 360 230 270 110 30 South Korea 100 330 470 60 40
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