Solution Manual For Mind On Statistics, 5th Edition

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Complete Solutions ManualMind on StatisticsFIFTH EDITIONJessica M. UttsUniversity of California, IrvineIrvine, CARobert F. HeckardPennsylvania State UniversityState College, PA

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ContentsChapter 1.......................................................................................................................................... 3Chapter 2.......................................................................................................................................... 9Chapter 3........................................................................................................................................ 45Chapter 4........................................................................................................................................ 65Chapter 5........................................................................................................................................ 87Chapter 6...................................................................................................................................... 100Chapter 7...................................................................................................................................... 114Chapter 8...................................................................................................................................... 134Chapter 9...................................................................................................................................... 153Chapter 10.................................................................................................................................... 193Chapter 11.................................................................................................................................... 211Chapter 12.................................................................................................................................... 235Chapter 13.................................................................................................................................... 265Chapter 14.................................................................................................................................... 296Chapter 15.................................................................................................................................... 307Chapter 16.................................................................................................................................... 332Chapter 17.................................................................................................................................... 345

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Chapter 1 Solutions, 5th ed.Page 1 of 6CHAPTER 1EXERCISE SOLUTIONS1.1a.The fastest speed was 150 miles per hour.b.The slowest speed driven by a male was 55 miles per hour.c.1/4 of the females reported having driven at 95 miles per hour or faster. Notice that 95 mph is theupperquartilefor females. By definition, about 1/4 of the values in a data set are greater than the upper quartile.d.1/2 of the females reported having driven 89 mph or faster. Notice that 89 mph is themedianvalue.e.1/2 of 102 = 51 females have driven 89 mph or faster.Note: For parts (d) and (e) the answer would have to be adjusted if there were any females who reported 89as their value, but from the data on page 2 we can see that there were not. Because there were no “ties”with the median, we know that exactly half of the values fall above it and half fall below it.1.2a.The median height is 65 inches.b.Range = Tallest – Shortest = 71 – 59 = 12 inches.c.The interval from 59 to 63.5 inches contains the shortest 1/4 of the women. This interval is from theminimum to the lower quartile.d.The interval from 63.5 to 67.5 inches contains the middle 1/2 of the women. This is an interval from thelower quartile to the upper quartile.1.3a.The observed rate of cervical cancer in Vietnamese American women is 86 per 200,000. This could alsobe expressed as 43 per 100,000 or 4.3 per 10,000, and so on. In decimal form, it is .00043.b.The risk of developing cervical cancer for Vietnamese American women in the next year is 86/200000 =.00043.c.The rate of 86 per 200,000 is based on past data and tells us the number of Vietnamese American whodeveloped cervical cancer out of a population of 200,000. The risk utilizes the rate from the past to tell usthe future likelihood of cervical cancer in other Vietnamese American women.1.4a.The base rate is about 13 in 1000, or about .013.b.The risk for men who smoke is just over 13 times the rate for non-smokers, or about .169.1.5a.All teens in the U.S. at the time the poll was taken.b.All teens in the U.S. who had dated at the time the poll was taken.1.6A population is a collection of all individuals of interest while a sample is a subset of the population ofinterest, for which measurements are taken in a study. In Case Study 1.6 the population of interest isprobably all men, and possibly women as well. However, the sample consisted of 22,071 male physicianswho volunteered for the study, so the population to which the results apply is all men similar to them.1.7a.All adults in the U.S. at the time the poll was taken.b.1.0311048or 3.1%c.34% ± 3.1%, or 30.9% to 37.1%.1.8a.The population is probably all Canadians who were eligible to participate in the survey (which isprobably all adults with telephones).b.There were 2000 people in the sample.c.022.200011nor 2.2%.d.In the sample, 16% viewed immigration as having a negative impact. The interval 16% ± 2.2%, or13.8% to 18.2% is 95% certain to cover the true percent of Canadians who viewed immigration as having anegative impact (at the time of the poll).1.9Solve fornin the equation11.0520n. Answer isn= 400 teenagers.3

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Chapter 1 Solutions, 5th ed.Page 2 of 61.10Solve fornin the equation30.1n. “Exact” answer is 11.11, which is not a possible sample size, soround up ton= 12 to guarantee a margin of error that’s less than 30%. Withn= 11, margin of error =30.1%.1.11a.This is an example of a self-selected or volunteer sample. Magazine readers voluntarily responded to thesurvey, and were not randomly selected.b.These results may not represent the opinions of all readers of the magazine. The people who respondprobably do so because they feel stronger about the issues (for example, violence on television or physicaldiscipline) than the readers who do not respond. So, they may be likely to have a generally different pointof view than those who do not respond.1.12The exercise did not specify what the survey is about, but no matter what, the survey is based on a self-selected sample, and people who feel strongly about the issues and/or who have extra time are more likelyto respond. The results will not be representative of all students who use the cafeteria.1.13a.Randomized experiment (because students were randomly assigned to the two methods).b.Observational study (because people cannot be randomly assigned to smoke or not).c.Observational study (because people cannot be randomly assigned to be a CEO or not).1.14a.Randomized experiment, because students were randomly assigned to receive Vitamin C or placebo.b.Observational study, because the patients are not randomly assigned to do anything. (Note that a randomsample is not the same thing as random assignment.)c.Randomized experiment, because participants were randomly assigned to meditation or low-fat diet.1.15Answers will vary, but one possibility is general level of activity. It is likely to differ for elderly peoplewho attend church regularly and those who don’t, and it is also likely to affect blood pressure. So it mightpartially explain the results of this study.1.16a.Number of courses might be a confounding variable. Students taking many courses may sleep less dueto the amount of work involved and may not do as well in school due to the load.b.Weight is not likely to be a confounding variable. Weight is probably not related either to amount ofsleep or to grades.c.Hours spent partying might be a confounding variable. Students who party a lot may sleep less, and mayalso get lower grades because they’re not studying.1.17You would need to know how large the difference in weight loss was for the two groups. If the differencein weight loss is very small (but not 0) it could be statistically significant, but not have much practicalimportance.1.18Statistical significance is when there is a relationship or difference that is large enough to be unlikely tohave occurred in the sample if there was no relationship or difference in the population of interest.Practical significance occurs when the relationship or difference is large enough to be important ormeaningful in a “real world” sense. A result can be statistically significant, but not practically significant.This may occur in studies with very large sample sizes.1.19You would want to know how many different relationships were examined. If this result was the only onethat was statistically significant out of many examined, it could easily be a false positive.1.20A false positive occurs when a relationship or difference is said to be statistically significant based onexamining information from a sample, but in fact there is no relationship or difference in the population.1.21The placebo group estimates the baseline rate of heart attacks for men not taking aspirin. So, the estimatedbaseline rate of heart attacks is 189/11,034, which is about 17 heart attacks per 1,000 men or 17/1000. (SeeTable 1.1 for the data.)4

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Chapter 1 Solutions, 5th ed.Page 3 of 61.22a.The amount of exercise per week is similar for men and women except that there are a few high valuesfor the men. The dotplot follows.Figure for Exercise 1.22ab.Women, median = 190 minutes.Men, median = 180 minutes.To find the median, put the data in order first.Forwomen, the ordered list of data is:0, 0, 0, 60, 60, 70, 100,180,200, 240, 240, 270, 300, 360, 360, 450The number of women is even (16), so the median is the average of the middle two values in the orderedlist. These middle two values, underlined and bold in the above list, are 180 and 200 and their average is190.Formen, the ordered list of data is:0, 0, 14, 60, 90, 120,180, 240, 300, 300, 360, 480, 600The number of men is odd (13) so the median is the middle value in the ordered data. This value,underlined and bold in the list above, is 180.c.Although the median response is different for women and men, the difference is only 10 minutes. Theweekly amount of exercise is about the same for the samples of women and men.1.23a.Minutes of exercise per weekMedian180Quartiles37330Extremes0600To determine the summary, first write the responses in order from smallest to largest.The ordered list of data is:0, 0, 14, 60, 90, 120, 180, 240, 300, 300, 360, 480, 600Minimum= 0 min.Maximum= 600 min.Median= 180 min.(middle value in the ordered list)Lower quartile= 42 min. It is the median of the values smaller than the median.These are 0, 0, 14, 60, 90, 120.Median of these six values is (14+70)/2 = 42.Upper quartile= 330 min. It is the median of the values larger than the median.Values larger than the median are 240, 300, 300, 360, 480, 600.Median of these values is (300+360)/2 = 330.b.Reported exercises hours per week for the men in the sample ranged from a low of 0 to a high of 600minutes per week. The median response was 180 min (3 hours). About 1/2 of the men (the middle half)reported exercising between 37 and 330 minutes (5 and a half hours) per week. About 1/4 said theyexercised less than 37 minutes per week while 1/4 said they exercised more than 330 minutes per week.1.24a.Minutes of exercise per weekMedian190Quartiles60285Extremes04505

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Chapter 1 Solutions, 5th ed.Page 4 of 6To determine the summary, first write the responses in order from smallest to largest.The ordered list of data is:0, 0, 0, 60, 60, 70, 100, 180, 200, 240, 240, 270, 300, 360, 360, 450Minimum= 0 min.Maximum= 450 min.Median= 190 min.(average of the middle two values in the ordered list, which are 180 and 200)Lower quartile= 60 min. It is the median of the values smaller than the median.These are 0, 0, 0, 60, 60, 70, 100, 180.Median of these eight values is (60+60)/2 = 60.Upper quartile= 285 min. It is the median of the values larger than the median.Values larger than the median are 200, 240, 240, 270, 300, 360, 360, 450.Median of these values is (270+300)/2=285.b.Reported exercise hours for the women in the sample ranged from a low of 0 to a high of 450 minutesper week. The median response was 190 min (3 hours and 10 minutes). About 1/2 of the women (themiddle half) reported exercising between 60 and 285 minutes per week. About 1/4 said they exercised lessthan 60 minutes per week while 1/4 said they exercised more than 285 minutes per week.1.25a.This is an observational study because vegetarians and non-vegetarians are compared and these groupsoccur naturally. People were not assigned to treatment groups.b.Since this is an observational study and not a randomized experiment, we cannot conclude that avegetarian diet causes lower death rates from heart attacks and cancer. Other variables not accounted formay be causing this reduction.c.This answer will differ for each student. One potential confounding variable is amount of exercise.This is a confounding variable because it may be that vegetarians also exercise more on average and thisled to lower death rates from heart attacks and cancer.1.26Base rates were not given. In this study, a base rate would be the actual rate (risk) of a particular cause ofdeath for people who are not vegetarians.1.27The base rate or baseline risk is missing from the report. You need to know the base rate of cancer of therectum for men to decide if the increased risk from drinking beer is large or small.1.28a.This was a randomized experiment because volunteers were randomly assigned to wear either a nicotinepatch or a placebo patch.b.You can conclude that use of nicotine patches leads to a higher success rate for those trying to quitsmoking than use of placebo patches.c.It was advisable to assign some of the patients to wear a placebo patch because then you can comparethe success rate of those patients to the success rate of the patients wearing nicotine patches. You will alsolearn in a future chapter that even though they have no active ingredients, placebos can have a largepsychological effect. Also, presumably people in the experiment want to quit smoking, so some willsucceed regardless of treatment method.1.29For Caution 1: Because the difference given in the previous exercise is a large difference (46% withnicotine patch and 20% with placebo), it has practical importance as well as statistical significance. ForCaution 2: Because the result is based on a randomized experiment, it is not possible that whether someonequit or not influenced the type of patch they were assigned.1.30In the study described in Exercise 1.28, data were gathered and analyzed in order to make a decision aboutthe effectiveness of the nicotine patch. This information will help individuals decide whether to wearnicotine patches when trying to quit smoking. Although the observed result was based only on a samplefrom a larger population, the data collection and analysis methods make it reasonable to conclude that thepatch is more effective than a placebo for the population represented by this sample.1.31Neither caution applies. The magnitude of the difference is given in Case Study 1.6, and considering thenumber of men between the ages of 40 and 84 in the United States population, the given difference has6

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Chapter 1 Solutions, 5th ed.Page 5 of 6practical importance. Because men were randomly assigned to take aspirin (or not) we can conclude thatthe correct direction of the cause and effect is that taking aspirin caused the reduction in heart attacks1.32a.The population is all University of California faculty members in 1995.b.The margin of error is approximately032.100011n, or roughly 3%.c.It cannot be concluded that a majority of all University faculty favored the criteria. In the sample a slightmajority (52%) was in favor, but the margin of error was about 3%. So, in the population the percent infavor could possibly be a minority (below 50%). An interval that is 95% certain to contain the percent inthe population is 52%3%, which is 49% to 55%. Because some values within this interval are below50%, we are not able to rule out the possibility that the percent in favor in the population is a minority.1.33a.The margin of error is about026.152511n.b.139.026, which is .113 to .165.This issample proportionmargin of error.1.34For someone 18 to 29 years old, the risk of seeing a ghost is 212/1525 = .139.1.35a.This is a self-selected (or volunteer) sample.b.Probably higher, because people who would say they have seen a ghost would be more likely to call thelate-night radio talk show than others. They might even be more likely to be listening to such a show.1.36a.Self-selected sample or volunteer sample.b.The results cannot be extended to any larger population because the sample was not selected to berepresentative of any population.1.37The term “data snooping” refers to looking at the data in a variety of ways until something interesting toreport emerges.1.38a.This statement has to be based on an observational study. The researchers observed who was breast-fedand who was not. It would not be possible to randomly assign mothers to breast-feed or not. It would not beethical to randomly assign this treatment.b.The better headline is “Link found between breast-feeding and school performance” because it does notimply that there is a cause-and-effect conclusion, while the other headline does. Because the study wasobservational, a cause-and-effect conclusion cannot be made. It is likely that children who were breast-fedas infants have other (confounding) factors in their lives that differ from children who were not, and thatmay influence school performance. For example, perhaps they are more likely to have mothers who don’twork, perhaps they are more likely to be first-born children, and so on. We can say that a link was found,but cannot say that breast-feedingleadsto better performance.1.39In some situations it is not practical or even possible to conduct a randomized experiment. For example, aresearcher may wish to study whether occupational exposure to asbestos affects the risk of lung disease. Itwould not be possible, or ethical, to assign people to occupations that involve differing amounts ofexposure to asbestos.1.40An observational study was done instead of an experiment because the researchers could not assignindividuals either to attend a religious service once a week and pray regularly or to not engage in thesepractices.1.41The answer will differ for students, but here is an example. Randomly assign volunteers to either eat lots ofchocolate or not eat any chocolate for a period of time, and give them a questionnaire about depression atthe beginning and the end of the time period. Then compare the change in depression scores for the twogroups.7

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Chapter 1 Solutions, 5th ed.Page 6 of 61.42a.Randomized experiment. People would not take a placebo as part of an observational study.b.Maybe not, because 20 side effects were tested so one or a few could appear to be a problem(statistically significant) just by chance even if none of them were a problem. In other words, it is possiblethat the observed relationship between taking aspirin and having headaches was a false positive.1.43USA Todaymade the mistake of making a cause-and-effect conclusion about the relationship betweenprayer and blood pressure. This conclusion is not justified because the data were from an observationalstudy. Specifically, they neglected to consider possible confounding variables like lifestyle choices, socialnetworks, and health of the people between the two groups. As a result, people may be led to believe that ifthey pray more often they will have lower blood pressure. That conclusion is not justified based on thisobservational study.1.44Step 1: The investigators asked if taking aspirin reduces the risk of a heart attack and then in theconclusion, asked to what population the results of this study apply.Step 2: They collected data from a five-year randomized experiment, including what treatment each doctorreceived (aspirin or placebo), and whether each doctor had a heart attack or not.Step 3: They summarized the data from step 2 by categorizing the doctors according to which type of pillthey took (aspirin or placebo). They then counted how many doctors in each treatment group had a heartattack. Further data analysis included calculating the “Attacks Per 1000 Doctors” for each group.Step 4: The investigators proceeded to make conclusions from the data given in Table 1.1. Specifically,they stated, “The results…support the conclusion that taking aspirin does indeed help reduce the risk ofhaving a heart attack. The rate of heart attacks in the group taking aspirin was only about half the rate ofheart attacks in the placebo group. In the aspirin group, there were 9.42 heart attacks per 1000 participatingdoctors, while in the placebo group, there were 17.13 heart attacks per 1000 participants.” They thencontinued to question if there were any other important risk factors or differences between the two groups.Step 5: The new knowledge is that this study has provided support for the benefit of aspirin in broaderpopulations concerning the reduction of the risk in heart attacks. As a result, millions of people take aspirinwith the hope that it will prevent a heart attack.8

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Chapter 2 Solutions, 5th ed.Page 1 of 36CHAPTER 2EXERCISE SOLUTIONS2.1a.4b.A state in the United States.c.n= 50.2.2a.2b.A randomly selected person.c.n= 620.2.3a.Whole population.b.Sample2.4a.Whole population.b.Sample2.5a.Population parameter.b.Sample statistic.c.Sample statistic.2.6a.Sample statistic.b.Population parameter.c.Sample statistic.2.7a.Sex and self-reported fastest ever driven speed.b.Students in a statistics class.c.The answer may vary. If you think the students represent a larger group of individuals, it is sample data.If interest is only in this group of students, or if you think these students do not represent any larger group,it is population data.2.8a.n= 2391.b.Individuals aged 65 years or older.c.Frequency of attending religious services and frequency of praying or reading the bible were related toblood pressure,.d.Sample data. They used the data to make generalizations about a larger population.2.9This is a population summary if we restrict our interest only to the fiscal year 1998. (If we were to use thisvalue to represent errors in other years, it could be considered to be a sample summary.)2.10a.Treatment used (placebo or aspirin) and whether individual died from heart attack or not.b.Male physicians between 40 and 84 years old.c.n= 22,071.d.Sample data. The used the data to make generalizations about a larger population.2.11a.Categorical.b.Quantitative.c.Quantitative.d.Categorical.2.12a.Quantitative.b.Categorical.c.Quantitative.d.Categorical.9

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Chapter 2 Solutions, 5th ed.Page 2 of 362.13a.Not ordinal. It’s categorical but the categories are not ordered.b.Ordinal. Grades are ordered categories.c.Not ordinal. It’s quantitative.2.14a.Continuous.All weights are possible within an interval of possibilities (although we can’t measureaccurately enough to observe all possibilities).b.Not continuous. The number of text messages must be an integer.c.Not continuous. The number of coins in a pocket would be an integer.2.15a.Explanatory variable is score on the final exam; response variable is final course grade.b.Explanatory variable is sex; response variable is opinion about the death penalty.2.16a.Not ordinal. It’s categorical but the categories are not ordered.b.Ordinal. The ratings are ordered.c.Not ordinal. It’s quantitative.2.17a.Not continuous. A student could not miss 4.631 classes for example.b.Continuous. With an accurate enough measuring instrument, any measurement is possible.c.Continuous. With an accurate enough time piece, any length of time is possible.2.18a.Explanatory variable is amount person walks or runs per day; response variable is the performance onthe lung test.b.Explanatory variable is age of the respondent; response variable is feeling about religious importance.2.19a.Whether a person supports the smoking ban or not is a categorical variable.b.Gains on verbal and math SATs are quantitative variables.2.20The explanatory variable is smoker or not. The response variable is Alzheimer sufferer or not.Bothvariables are categorical.2.21a.Sex and pulse rate.b.Sex is categorical, pulse rate is quantitative.c. Is there a difference between the mean pulse rates of men and women? The sample mean pulse rate foreach sex would be useful.2.22This will differ for each student. As an example, suppose a survey question about income only allowed theresponse categories 1 = under $20,000 and 2= $20,000 to $49,999 and 3= more than $49,999. The incomecategories are ordered, but so little is known about actual income that the mean response is meaningless.2.23This will differ for each student. One example where numerical summaries would make sense for anordinal variable is the response to the question “What grade do you expect in this class? 1=A, 2=B, 3=C,4=D, 5=F.” The mean numerical response is an expected class GPA.2.24This will differ for each student.2.25a.A unit is a person. Dominant hand is a categorical variable and IQ is a quantitative variable. Explanatoryvariable is dominant hand and response variable is IQ .b.A unit is a married couple. Eventual divorce status and pet ownership are both categorical variables.Explanatory variable is pet ownership and response variable is eventual divorce status.2.26a.A unit is a college student. GPA and hours of study each week are both quantitative variables.Explanatory variable is hours of study and response variable is GPA.b.A unit is a tax-paying individual in the United States. Tax bracket is an ordinal variable and percentagedonated to charities is a quantitative variable. Explanatory variable is tax bracket and response variable ispercentage donated to charities.10

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Chapter 2 Solutions, 5th ed.Page 3 of 362.27a.1427/2530 = .564, which is 56.4%.b.1 – (1427/2530) = .436, which is 43.6%.c.Never: 105/2530 = .042 (4.2%);Rarely: 248/2530 = .098 (9.8%); Sometimes: 286/2530 = .113 (11.3%).Most times: 464/2530 = .183 (18.3%); Always: 1427/2530 = .564 (56.4%)d.Figure for Exercise 2.27d2.28a.ResponseFrequencyRelative frequencyVery happy599599/2015 = .297 (29.7%)Pretty happy11001100/2015 = .546 (54.6%)Not too happy316316/2015= .157 (15.7%)Total20151 (100%)b.Figure for Exercise 2.28bNot too happyPretty happyVery happy6050403020100ResponsePercent15.754.629.7c.29.7% + 54.6% = 84.3%2.29a.Preferred use of cell phoneTo talkTo textTotalWomen22 (20.8%)84 (79.2%)106 (100%)Men34 (41.0%)49 (59.0%)83 (100%)11

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Chapter 2 Solutions, 5th ed.Page 4 of 36b.Women: 20.8% to talk, 79.2% to textc.Men: 41.0% to talk, 59.0% to textd. Women were more likely to say “to text” than men whereas men were more likely to say “to talk.”2.30a.1700/2470 = .688, or 68.8%b.1056/1700 = .621, or 62.1%c.300/657 = .457, or 45.7%d.41/113 = .363, or 36.3%2.31a.Explanatory variable is whether a person smoked or not. Response variable is whether they developedAlzheimer’s or not.b.Explanatory variable is political party. Response variable is whether a person voted or not.c.Explanatory variable is income level. Response variable is whether a person has been subjected to a taxaudit or not.2.32a.Figure for Exercise 2.32a35 and Over30-3425-2920-24Under 20302520151050AgePerceent8.115.724.730.620.9b.Figure for Exercise 2.32b35 and Over8.1%30-3415.7%25-2924.7%20-2430.6%Under 2020.9%12

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Chapter 2 Solutions, 5th ed.Page 5 of 36c.The pie chart may more effectively show that there are three age groups with large percentages, and itmay be faster to read these percentages than with the bar chart. One problem, however, is that the agegroups are shown in a circular pattern, an unnatural way to view the age. The bar chart gives a better senseof the distribution of ages because the ages are shown along a more natural horizontal number line.2.33a.The explanatory variable is sex and the response variable is how they feel about their weight.b.c.Feeling overweight: 38/143 = .266, or 26.6%; right weight: 99/149 = .692, or 69.2%;underweight: 6/149 = .042, or 4.2%.d.Feeling overweight: 18/78 = .231, or 23.1%; right weight: 35/78 = .449, or 44.9%;underweight: 25/78 = .321 or 32.1%.e.Males are more likely than females to feel that they are underweight; females are more likely than malesto say that their weight is about right.2.34Figure for Exercise 2.342.35a.Picked SPicked QTotalS listed first613192Q listed first455398Total10684190b.Picked S=%3.66%100)92/61(; Picked Q=%7.33%100)92/31(;c.Picked S=%9.45%100)98/45(; Picked Q=%1.54%100)98/53(;Feelings About WeightSexOverweightAbout rightUnderweightTotalFemale38 (26.6%)99 (69.2%)6 (4.2%)143Male18 (23.1%)35 (44.9%)25 (32.1%)7813

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Chapter 2 Solutions, 5th ed.Page 6 of 36d.Figure for Exercise 2.35de. Parts (b) and (c) show that the percentage picking S was higher when S was listed first than when Q waslisted first. It looks like the letter picked was influenced by the letter listed first.2.36a.The columns can be labeled “Picked 1stletter” and “Picked 2ndletter.” In the “S listed first” row, list thecounts in the same order as in the table for Exercise 2.35(a). In the “Q listed first” row, the count for “Qpicked” should be in the “Picked 1stletter” column (because Q was the first letter). The table isPicked 1stletterPicked 2ndletterTotalS Listed First61 (66%)31 (34%)92Q Listed First53 (54%)45 (46%)98All114 (60%)76 (40%)190b.A bar chart of percentages picking first and second letters given on each form of the question (rowpercentages in the table above) along with these percentages for the overall sample follows:Figure for Exercise 2.36bc.The variables used in this exercise are more appropriate for illustrating the point of this data set. Thequestion of interest is whether participants might be more likely to pick the fist letter given than the secondregardless of whether it was an S or Q. The bar chart given for part (b) illustrates that the fist letter listedwas picked more often for both forms.2.37a.The fastest speed was 150 miles per hour.14

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Chapter 2 Solutions, 5th ed.Page 7 of 36b.The slowest speed driven by a male was 55 miles per hour.c.1/4 of the females reported having driven at 95 miles per hour or faster. Notice that 95 mph is theupperquartilefor females. By definition, about 1/4 of the values in a data set are greater than the upper quartile.d.1/2 of the females reported having driven 89 mph or faster. Notice that 89 mph is themedianvalue.e.1/2 of 102 = 51 females have driven 89 mph or faster.2.38a.The median value is 110 mph for males, compared to 89 mph for females.b.The spread is about the same for the two sexes.The spread of the extremes is 150−55 = 95 mph for themales, compared to 130 – 30 = 100 mph for the females. The spread of the quartiles is slightly greater formales (120 – 95 = 25 for males, compared to 95-80 = 15 for females.)2.39a.The center for the females is at a greater percentage than it is for the males. For females the center looksto be somewhere around 27%. For males, the center looks to be a bit less than 18%.b.The data are more spread for the females.c.The greatest two female percentages are set apart from the bulk of the data. The values are about 65%and 72%.2.40a.Median height = 65 inches.b.Range = Tallest – Shortest = 71 – 59 = 12 inches.c.The interval from 59 to 63.5 inches contains the shortest 1/4 of the women.This interval is from the minimum to the lower quartile.d.The interval from 63.5 to 67.5 inches contains the middle 1/2 of the women.This is an interval from the lower quartile to the upper quartile.2.41a.The median value, 65 inches, describes the location.b.The interval described by the extremes, 59 to 71 inches, describes spread. We might also describe spreadusing the interval 63.5 to 67.5, the spread of the middle 50% of the data.2.42a.The dataset is skewed to the right (it stretches in that direction).b.The value 13 looks to be an outlier. It is separate from the bulk of the data.c.2 ear pierces was the most reported value. About 44 or so women said they had this many ear pierces.d.About 32 or so women said they had 4 ear pierces.2.43a.The dataset looks approximately symmetric and bell-shaped.b.There are no noticeable outliers.c.The most frequently reported value for sleep was 7 hours.d.Roughly 14 or so students said they slept 8 hours the previous night.2.44a.Two slightly different versions of the histogram are shown below.In the first, the bars touch each other;in the second, the bars are separated and labeled with the category limits. The first histogram looks a littlenicer but there could be confusion about the exact endpoints of intervals. Notice that we have shown afrequency axis on the left and the corresponding relative frequency (percentage) axis on the right.15

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