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statistics principles and methods
Statistics The Exploration And Analysis Of Data 6th Edition John M Scheb, Jay Devore, Roxy Peck - Solutions
=+drivers exceed the speed limit by more than do female teenage drivers?Amount by Which Speed Limit Was Exceeded Male Female Driver Driver 1.3 20.2 1.3 0.5 0.9 1.1 2.1 0.7 0.7 1.1 1.3 1.2 3 0.1 1.3 0.9 0.6 0.5 2.1 0.5
=+a. Data consistent with summary quantities appearing in the paper are given in the accompanying table. The measurements represent the difference between the observed vehicle speed and the posted speed limit (in miles per hour) for a sample of male teenage drivers and a sample of female teenage
=+490 C h a p t e r 11 ■ Comparing Two Populations or Treatments Bold exercises answered in back ● Data set available online but not required ▼ Video solution available Percent of Time Female Monkeys Male Monkeys Sample Sample Sample Standard Sample Standard n Mean Deviation n Mean Deviation
=+school. Assume that it is reasonable to regard the teen drivers in this study as representative of the population of teen drivers. Use a .01 level of significance for any hypothesis tests.1 2
=+observing their vehicles as they left a high school parking lot and then again at a site approximately mile from the
=+11.12 ● The paper “The Observed Effects of Teenage Passengers on the Risky Driving Behavior of Teenage Drivers” (Accident Analysis and Prevention [2005]: 973–982) investigated the driving behavior of teenagers by
=+e. Explain why it would be inappropriate to use the twosample t test to decide if there was evidence that the mean percentage of the time spent playing with the police car and the mean percentage of the time spent playing with the doll is not the same for female monkeys.
=+d. Based on the conclusions from the hypothesis tests of Parts (a)–(c), is the quoted newspaper story headline a reasonable summary of the findings? Explain.
=+b. Consider the average miles per hour over the speed limit for teenage drivers with passengers shown in the accompanying table. For purposes of this exercises, suppose that each driver-passenger combination mean is based on a sample of size n 5 40 and that all sample standard deviations are
=+i. Is there sufficient evidence to conclude that the average number of miles per hour over the speed limit is greater for male drivers with male passengers than it is for male drivers with female passengers?
=+germ, the part of the kernel located at the bottom center of the kernel that is used to produce corn oil, partially removed) and corn meal made from corn that has not been degermed. Specimens of corn meal were analyzed and the total fumonisin level (ppm) was determined for each specimen.
=+11.14 Fumonisins are environmental toxins produced by a type of mold and have been found in corn and in products made from raw corn. The Center for Food Safety and Applied Nutrition provided recommendations on allowable fumonisin levels in human food and in animal feed based on a study of corn
=+Based on these results, is there evidence that taking 40 mg of ginkgo three times a day is effective in increasing mean performance on the Wechsler Memory Scale? Test the relevant hypotheses using a 5 .05.
=+for six weeks. The 115 participants assigned to the control group took a placebo pill three times a day for six weeks.At the end of six weeks, the Wechsler Memory Scale (a test of short-term memory) was administered. Higher scores indicate better memory function. Summary values are given in the
=+11.13 Many people take ginkgo supplements advertised to improve memory. Are these over-the-counter supplements effective? In a study reported in the paper “Ginkgo for Memory Enhancement” (Journal of the American Medical Association [2002]: 835–840), elderly adults were assigned at random
=+c. Write a few sentences commenting on the effect of a passenger on a teen driver’s speed.
=+iii. Is there sufficient evidence to conclude that the average number of miles per hour over the speed limit is smaller for male drivers with female passengers than it is for female drivers with male passengers?
=+ii. Is there sufficient evidence to conclude that the average number of miles per hour over the speed limit is greater for female drivers with male passengers than it is for female drivers with female passengers?
=+Calculate a 99% confidence interval for the difference between males and females in mean number of science courses planned. Interpret your interval. Based on your interval, how would you answer the question posed at the beginning of the exercise?
=+This was true for men, t(64) 5 3.75, p , .001, and for women, t(29) 5 2.26, p , .05.”
=+to conclude that the proportion very satisfied is different for elementary school teachers than it is for high school teachers? Test the appropriate hypotheses using a .05 significance level.
=+11.72 Do teachers find their work rewarding and satisfying? The article “Work-Related Attitudes” (Psychological Reports [1991]: 443–450) reported the results of a survey of random samples of 395 elementary school teachers and 266 high school teachers. Of the elementary school teachers,
=+changes was 11.45 lb. Is there sufficient evidence to conclude that the true mean change in weight is positive?Use a 5 .05.
=+Three hundred twenty-two subjects, selected at random from those who successfully participated in a program to quit smoking, were weighed at the beginning of the program and again 1 year later. The mean change in weight was 5.15 lb, and the standard deviation of the weight Specimen Direct
=+11.71 Many people who quit smoking complain of weight gain. The results of an investigation of the relationship between smoking cessation and weight gain are given in the article “Does Smoking Cessation Lead to Weight Gain?”(American Journal of Public Health [1983]: 1303–1305).
=+Do the data provide sufficient evidence to conclude that the mean number of seeds detected differs for the two methods? Test the relevant hypotheses using a 5.05.
=+An article in the Journal of Ecology (“A Comparison of Methods for Estimating Seed Numbers in the Soil”[1990]: 1079–1093) considered three such methods. The accompanying data give number of seeds detected by the direct method and by the stratified method for 27 soil specimens.
=+11.70 ● Several methods of estimating the number of seeds in soil samples have been developed by ecologists.
=+11.74 Gender differences in student needs and fears were examined in the article “A Survey of Counseling Needs of Male and Female College Students” (Journal of College Student Development [1998]: 205–208). Random samples of male and female students were selected from those attending a
=+11.77 Are college students who take a freshman orientation course more or less likely to stay in college than those who do not take such a course? The article “A Longitudinal Study of the Retention and Academic Performance of Participants in Freshmen Orientation Courses”(Journal of College
=+who agreed that celibacy should be a matter of personal choice declined from 1985 to 1993? Use a 5 .05.
=+1993. The priests surveyed were asked whether they agreed with the following statement: Celibacy should be a matter of personal choice for priests. In 1985, 69% of those surveyed agreed; in 1993, 38% agreed. Suppose that the samples were randomly selected and that the sample sizes were both
=+11.76 An Associated Press article (San Luis Obispo Telegram-Tribune, September 23, 1995) examined the changing attitudes of Catholic priests. National surveys of priests aged 26 to 35 were conducted in 1985 and again in
=+humanities) with a HOPE scholarship lost the scholarship at the end of the first year because they had a GPA of less than 3.0. It was also reported that 72 of a random sample of 111 students entering the College of Computing with a B average had lost their HOPE scholarship by the end of the first
=+53.2% of a random sample of 137 students entering Ivan Allen College at Georgia Tech (social science and
=+11.75 The state of Georgia’s HOPE scholarship program guarantees fully paid tuition to Georgia public universities for Georgia high school seniors who have a B average in academic requirements as long as they maintain a B average in college. (See “Who Loses HOPE? Attrition from Georgia’s
=+27.5% said that they were concerned about the possibility of getting AIDS. Of 568 female students surveyed, 42.7%reported being concerned about the possibility of getting AIDS. Is there sufficient evidence to conclude that the proportion of female students concerned about the possibility of
=+c. Test the hypothesis that there was no change in the mean number of drinks between 1994 and 1995 for the non-credit card shoppers. Be sure to calculate and interpret the P-value for this test.
=+b. Calculate a 95% confidence interval for the mean difference in drink consumption for credit card shoppers between 1994 and 1995. Is there evidence that the mean number of drinks decreased?
=+11.66 The article “Workaholism in Organizations: Gender Differences” (Sex Roles [1999]: 333–346) gave the following data on 1996 income (in Canadian dollars) for random samples of male and female MBA graduates from a particular Canadian business school:n s
=+b. Do students who don’t return have a lower mean personal contact rating than those who do return? Test the relevant hypotheses using a significance level of .01.
=+a. Construct and interpret a 95% confidence interval for the difference in mean campus involvement rating for returning and nonreturning students. Does your interval support the statement that students who do not return are less involved, on average, than those who do? Explain.
=+rated themselves on personal contact and campus involvement. The resulting data are summarized here:Returning Nonreturning(n 5 48) (n 5 42)Standard Standard Mean Deviation Mean Deviation Personal Contact 3.22 .93 2.41 1.03 Campus Involvement 3.21 1.01 3.31 1.03
=+11.65 The article “So Close, Yet So Far: Predictors of Attrition in College Seniors” (Journal of College Student Development [1999]: 343–354) attempts to describe differences between college seniors who disenroll before graduating and those who do graduate. Researchers randomly selected
=+c. Do you have enough information to carry out a test to determine whether there is a significant difference in the mean testosterone levels of male and female trial lawyers?If so, carry out such a test. If not, what additional information would you need to be able to conduct the test?
=+b. Based on the information given, is there a significant difference in the mean testosterone level for female trial and nontrial lawyers?
=+a. Based on the information given, is there a significant difference in the mean testosterone level for male trial and nontrial lawyers?
=+Males 258 $133,442 $131,090 Females 233 $105,156 $98,525
=+a. For what significance levels would you conclude that the mean salary of female MBA graduates of this business school is above $100,000?
=+a. The standard deviation of the difference was quite large. Explain how this could be the case.
=+had consumed during the previous week. A year later (after liquor stores started accepting credit cards for purchases), these same individuals were again asked how many drinks they had consumed in the previous week.The data shown are consistent with summary statistics presented in the
=+11.69 As part of a study to determine the effects of allowing the use of credit cards for alcohol purchases in Canada(see “Changes in Alcohol Consumption Patterns Following the Introduction of Credit Cards in Ontario Liquor Stores,” Journal of Studies on Alcohol [1999]: 378–382), randomly
=+number of words recalled after 1 hr exceeds the mean recall after 24 hr by more than 3? Use a level .01 test.Subject 1 2 3 4 5 6 7 8 1 hr later 14 12 18 7 11 9 16 15 24 hr later 10 4 14 6 9 6 12 12
=+11.68 ● In a study of memory recall, eight students from a large psychology class were selected at random and given 10 min to memorize a list of 20 nonsense words. Each was asked to list as many of the words as he or she could remember both 1 hr and 24 hr later, as shown in the accompanying
=+used to arrive at an approval score, with higher scores indicating greater approval. A random sample of 56 male players resulted in a mean approval rating for unsportsmanlike play of 2.76, whereas the mean for a random sample of 67 female players was 2.02. Suppose that the two sample standard
=+11.67 The article “The Relationship of Task and Ego Orientation to Sportsmanship Attitudes and the Perceived Legitimacy of Injurious Acts” (Research Quarterly for Exercise and Sport [1991]: 79–87) examined the extent of approval of unsporting play and cheating. High school basketball
=+b. Is there convincing evidence that the mean salary for female MBA graduates of this business school is lower than the mean salary for the male graduates?
=+the difference in the proportion returning for students who do not take an orientation course and those who do. Give an interpretation of this interval.
=+c. Do the data suggest that the true mean GPA for students hired by the university as resident assistants differs from the mean for students who are not hired? Test the relevant hypotheses using a 5 .05.
=+b. Do the data suggest that the true mean leadership score for students hired by the university as resident assistants differs from the mean for students who are not hired? Test the relevant hypotheses using a 5 .05.
=+a. Do the data suggest that the true mean self-esteem score for students hired by the university as resident assistants differs from the mean for students who are not hired?Test the relevant hypotheses using a 5 .05.
=+those who were not hired (“Wellness as a Factor in University Housing,” Journal of College Student Development[1994]: 248–254), as shown in the accompanying table.Self-Esteem Leadership GPA s s s Hired (n 5 69) 83.28 12.21 62.51 3.05 2.94 .61 Not Hired (n 5 47) 81.96 12.78 62.43 3.36 2.60
=+11.86 Data on self-esteem, leadership ability, and GPA were used to compare college students who were hired as resident assistants at Mississippi State University and
=+Is there sufficient evidence to conclude that teenage boys score higher on the Worries Scale than teenage girls? Use a significance level of a 5 .05.
=+results are summarized in the accompanying table.Sample Sample Gender n Mean Score sd Girls 108 62.05 9.5 Boys 78 67.59 9.7
=+11.85 Do teenage boys worry more than teenage girls?This is one of the questions addressed by the authors of the article “The Relationship of Self-Esteem and Attributional Style to Young People’s Worries” (Journal of Psychology [1987]: 207–215). A scale called the Worries Scale was
=+11.87 The article “Religion and Well-Being Among Canadian University Students: The Role of Faith Groups on Campus” (Journal for the Scientific Study of Religion[1994]: 62–73) compared the self-esteem of students who belonged to Christian clubs and students who did not belong to such
=+self-esteem. The same questionnaire was also completed by each student in a random sample of n 5 124 students who did not belong to a religious club (the unaffiliated group). The mean self-esteem score for the affiliated
=+a. Compute a 90% confidence interval for the true average difference between surface and subsoil pH for agricultural land in this county.
=+11.90 ● Samples of both surface soil and subsoil were taken from eight randomly selected agricultural locations in a particular county. The soil samples were analyzed to determine both surface pH and subsoil pH, with the results shown in the accompanying table.Location 1 2 3 4 5 6 7 8 Surface
=+Of those deaf from birth, 75 had removed the implant, whereas only 25 of those who went deaf after learning to speak had done so. Does this suggest that the true proportion who remove the implants differs for those that were born deaf and those that went deaf after learning to speak?Test the
=+11.89 An electronic implant that stimulates the auditory nerve has been used to restore partial hearing to a number of deaf people. In a study of implant acceptability (Los Angeles Times, January 29, 1985), 250 adults born deaf and 250 adults who went deaf after learning to speak were followed
=+Is there any difference between the true proportions of yes responses to these questions? Can a procedure from this chapter be used to answer the question posed? If yes, use it; if not, explain why not.
=+then asked of each individual in the same sample: “Do you do any sports or hobbies involving physical activities, or any exercise, including walking, on a regular basis?” The resulting data are shown in the accompanying table.Yes No Initial Question 48 52 Revised Question 60 40
=+11.88 Key terms in survey questions too often are not well understood, and such ambiguity can affect responses. As an example, the article “How Unclear Terms Affect Survey Data” (Public Opinion Quarterly [1992]: 218–231) described a survey in which each individual in a sample was asked,
=+group was 25.08, and the mean for the unaffiliated group was 24.55. The sample standard deviations weren’t given in the article, but suppose that they were 10 for the affiliated group and 8 for the unaffiliated group. Is there evidence that the true mean self-esteem score differs for
=+b. Is there sufficient evidence to indicate that true mean pulse rate in a dental setting differs from the true mean pulse rate in a medical setting? Use a significance level of .05.
=+a. Do the data strongly suggest that true mean blood pressure is higher in a dental setting than in a medical setting?Use a level .01 test.
=+If we view the 41 games with Gretzky as a random sample of all Oiler games in which Gretzky played and the 17 games without Gretzky as a random sample of all Oiler games in which Gretzky did not play, is there evidence that the mean number of goals scored by the Oilers is higher for games in
=+11.81 Wayne Gretzky was one of ice hockey’s most prolific scorers when he played for the Edmonton Oilers.During his last season with the Oilers, Gretzky played in 41 games and missed 17 games due to injury. The article“The Great Gretzky” (Chance [1991]: 16–21) looked at the number of
=+with fluoridated water had decayed teeth. Let p1 denote the true proportion of children drinking fluoridated water who have decayed teeth, and let p2 denote the analogous proportion for children drinking unfluoridated water. Estimate p1 2 p2 using a 90% confidence interval. Does the interval
=+11.80 The positive effect of water fluoridation on dental health is well documented. One study that validates this is described in the article “Impact of Water Fluoridation on Children’s Dental Health: A Controlled Study of Two Pennsylvania Communities” (American Statistical Association
=+games with a player suffering a sliding injury? Answer by performing a level .01 test. What assumptions are necessary in order for your test to be valid? Do you think they are reasonable in this case?
=+Does the use of breakaway bases reduce the proportion of
=+11.79 The article “Softball Sliding Injuries” (American Journal of Diseases of Children [1988]: 715–716) provided a comparison of breakaway bases (designed to reduce injuries) and stationary bases. Consider the accompanying data (which agree with summary values given in the paper).Number
=+Number Who Use n Marijuana Exposed to DARE 288 141 Not Exposed to DARE 335 181
=+11.82 Here’s one to sink your teeth into: The authors of the article “Analysis of Food Crushing Sounds During Mastication: Total Sound Level Studies” (Journal of Texture Studies [1990]: 165–178) studied the nature of sounds generated during eating. Peak loudness (in decibels at 20 cm
=+Forty subjects participated, with ten assigned at random to each combination of conditions (such as closed-mouth, potato chip, and so on). We are not making this up! Summary values taken from plots given in the article appear in the accompanying table.n s Potato Chip Open mouth 10 63 13 Closed
=+The analogous differences were also calculated for pulse rates. Summary data follows.
=+11.84 Dentists make many people nervous (even more so than statisticians!). To see whether such nervousness elevates blood pressure, the blood pressure and pulse rates of 60 subjects were measured in a dental setting and in a medical setting (“The Effect of the Dental Setting on Blood Pressure
=+the mean number of imitations is higher for infants who watch a human model than for infants who watch a doll?Test the relevant hypotheses using a .01 significance level.Person Doll Model Model 5.14 3.46 s 1.60 1.30
=+was mouth opening. This action was modeled repeatedly by either a person or a doll, and the number of times that the infant imitated the behavior was recorded. Twentyseven infants participated, with 12 exposed to a human model and 15 exposed to the doll. Summary values are given here. Is there
=+11.83 Are very young infants more likely to imitate actions that are modeled by a person or simulated by an object? This question was the basis of a research study summarized in the article “The Role of Person and Object in Eliciting Early Imitation” (Journal of Experimental Child Psychology
=+c. The means and standard deviations given here were actually for stale chips. When ten measurements of peak loudness were recorded for closed-mouth chewing of fresh tortilla chips, the resulting mean and standard deviation were 56 and 14, respectively. Is there sufficient evidence to conclude
=+b. For closed-mouth chewing (the recommended method!), is there sufficient evidence to indicate that there is a difference between potato chips and tortilla chips with respect to mean peak loudness? Test the relevant hypotheses using a 5 .01.
=+a. Construct a 95% confidence interval for the difference in mean peak loudness between open-mouth and closedmouth chewing of potato chips. Interpret the resulting interval.x
=+b. What assumptions are necessary to validate the interval in Part (a)?
=+to take in the future, and they also indicated the number of science courses they thought boys their age should take in the future. For each girl, the authors calculated the difference between the number of science classes she intends to take and the number she thinks boys should take.
=+11.52 The article “Spray Flu Vaccine May Work Better Than Injections for Tots” (San Luis Obispo Tribune, May 2, 2006) described a study that compared flu vaccine
=+b. What potential source of bias might limit your ability to generalize the estimate from Part (a) to the populations of all cardiologists and all internists?
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