Solution Manual For The Basic Practice of Statistics, 8th Edition

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Chapter 0–Getting Started0.1 (a)More than likely, the individuals who chose to take vitamin E were more health-consciousin general than those who didn’tchoose to take it. The vitamin E takers may alsohave been more affluent (had money available to purchase the vitamins and, possibly, hadbetter health care generally).(b)In a randomized experiment, people of all types arerandomly assigned to the treatments. This means that poorer, less healthy people are inboth treatment groups, as are wealthier, healthier people.0.2Overall, most of this period (about 1940−1974) had falling gas prices. However,instances of rapid price increases also occurred: 1931−1932 (due to policies intended to“correct” the Depression), 1974−1975 (the Arab oil embargo), and 1979−1980 (Mideasttensions and the overthrow of the Shah of Iran). Interestingly, the start of World War II didnot correspond to a spike in prices (perhaps due to rationing), but an increase occurred inthe late 1940s, which could correspond to war veterans being able to purchase cars.0.3 (a)The proportion of Americans who feel this way is very likely much lower. The“survey” was one of voluntary response (people were not randomly selected but madetheir own decision about whetherto participate). Those who knew about the “poll” had justwatched Mr. Schultz’s“lengthy and impassioned”monologue and were primed to agreewith him.(b)As long as the poll was one of voluntary response, the sample size (868;2,500; or100,000) doesn’t matter; itis a biased sample and will not reflect the views ofpeople nationwide.0.4 (a)We can tell that the last three months of 2001 were unusual because the dots forthese months are at the top of the bars.(b)The terrorists themselves didn’t cause the fatalcrashes. After the attacks of 9/11, people (if they traveled at all) were reluctant to fly. Thus,if they really needed to travel (such as for Thanksgiving or Christmas), they traveled by car.With more car travel, car crashes occurred more often.

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Chapter 1 – Picturing Distributions with Graphs1.1 (a)The individuals are the car makes and models.(b)For each individual, thevariables recorded are: vehicle class (categorical), transmission type (categorical),number of cylinders (usually treated as quantitative), city mpg (quantitative),highway mpg (quantitative), and annual fuel cost in dollars (quantitative).1.2Answers will vary. Some possible categorical variables: whether or not thestudent plays sports; sex; whether or not the student smokes; and attitude aboutexercise. Some possible quantitative variables: weight (kilograms or pounds), height(centimeters or inches); resting heart rate (beats per minute); and body mass index(kg/m2or lb/ft2).1.3 (a)91% use these top social media sites; 9% use other sites most often.(b)Abar graph is provided.(c)If you include an “Other” category, then a pie chart is appropriate. This surveyasked about the site used most often, so each individual is only represented in onecategory, and the categories make up the whole.01020304050FacebookInstagramSnapchatTwitterGoogle+PinterestOtherPercentageSocial media sitePercent Used Most Often Among Americans Aged 12—24

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1.4 (a)Individuals fall into more than one of the categories.(b)A bar graph isshown.

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1.5A pie chart can be made because the days are non-overlapping and make up thewhole. Some births are scheduled (induced labor, for example) and, probably, mostare scheduled for weekdays.1.6Make this histogram by hand, as the instructions suggest.1.7Use the applet to answer these questions.1.8The distribution is slightly right-skewed. The center is between 30% and 40%(23 states have less than 30% minority residents, and another 10 states havebetween 30% and 40%). The statewide percents range from about 0% to about80%. No states have an unusually large or small percent of minority residents.1.9 (a)There are two clear peaks in the distribution. If we gave only one center, itwould most likely be between these and not be truly representative.(b)Young boysmight spend a lot of time outdoors playing; their time outside in places where theywould encounter ticks might well be less in younger adulthood. With families andyard work, their time outside might increase.(c)No, this is incorrect. Hiking in thewoods at any age will make a person more likely to encounter the ticks that spreadLyme disease.(d)The histograms have the same shapes, but females have a slightlylower incidence rate until age 65, after which females have a slightly higher rate.Females under age 65, possibly, spend less time outdoors in areas where they wouldencounter ticks.

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1.10(a)A stemplot is provided. With a single stem, the distribution appearedunimodal. After splitting the stems, it appears bimodal.088911155678920223333332677830111435799401112458851112234561677775(b)The histogram with bins of width 5 will give the same pattern as the stemplotfrom part (a).

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1.11Here is a stemplot for health expenditure per capita (in PPP). Data are roundedto units of hundreds. For example, Argentina’s 1725 becomes 17. Stems arethousands and are split, as prescribed. This distribution is right-skewed, with asingle high outlier (United States). There seem to be two clusters of countries. Thecenter of this distribution is around 20 ($2000 spent per capita). The distributionvaries from 0|2 (about $200 spent per capita) to 9|1 (about $9100 spent per capita).0223067789111141566772242831337422345688955662367788911.12 (a)A time plot of average tuition and fees is given.(b)Average tuition and fees have steadily climbed during the 35-year period, withsharpest absolute increases between 2009 and 2012.(c)Average tuition and feeshave not decreased (as shown in this plot), but there have been periods of verysmall increases (1995–2000 and 2012–2013, for example). There are two periods ofvery rapid increases: 2000–2005 and 2008–2012.(d)It would be better to usepercent increases rather than dollar increases. A 10% increase in average tuition

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and fees in 1980 should correspond to a 10% increase in average tuition and fees in2005, but the absolute dollar increases in these cases are very different.1.13(a) the students.1.14(c) a bar graph but not a pie chart. Individuals could belong to more than onecategory.1.15(b) Square footage and average monthly gas bill are both quantitativevariables.1.16(b) categorical variable. Zip codes are equivalent to town (or zone) names oridentifications, and you can’t do arithmetic meaningfully with them.1.17(b) 88% to 92%.1.18(b) 2, 3, 4, 5, 6, 7, 8, 9.1.19(b) 76%. There are 50 observations, so the center would be between the 25thand 26thobservations; both of these are 76%.1.20(a) skewed to the left.1.21(c) 34% enrolled. The stems are rounded to whole percents; you cannot makefiner judgments.1.22(c) skewed to the right.1.23 (a)Individuals are students who have finished medical school.(b)Five, inaddition to “Name.” “Age” (in years) and “USMLE” (in score points) are quantitative.The others are categorical.1.24The categorical variables are freezer type and Energy Star compliant (yes/no).The quantitative variables are annual energy consumption (kw), width (in), depth(in), height (in), freezer capacity (ft3), and refrigerator capacity (ft3). The individualsare the refrigerator makes and models.

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1.25“Other colors” should account for 2%. A bar graph would be an appropriatedisplay. If you included the “Other” category, a pie chart could also be made.1.26 (a)A bar graph for the percent who used any tobacco product is given. Thepercent stayed relatively constant, with a slight decrease from 2011 to 2013 andincreasing since.21222324252620112012201320142015PercentageYearPercentage of High Schoolers Who UsedAny Tobacco Product in Last 30 Days

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(b)See the bar chart given.(c)The plot in part (b) shows that the recent increase in tobacco usage is due to adrastic increase in the use of e-cigarettes. Usage of other forms of tobacco hasdecreased since 2011.1.27 (a)A bar graph is given.(b)Yes, we can construct a pie chart if we provide an "Other" category, where thetotal number of deaths in the "Other" category is 28486-11619-4878-4329-1496-1170-362=4632. The creation of an "Other" category is required for a pie chart sothat the number of deaths in each subcategory sum to the total number of deaths.Without an "Other" category, we cannot construct a pie chart.1.28About 20% had debt between $25,000 and $49,999. Less than 5% had debtabove $150,000, but it is hard to tell from the plot.05101520CigarettesCigarsPipesSmokelesstobaccoE-cigarettesPercentagePercentage of High Schoolers Who UsedTobacco20112012201320142015

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1.29 (a)A bar graph is provided.(b)For the 18–34 age group, the hours are roughly equal. For the older age groups,social apps are used more often than entertainment apps.(c)A pie chart is notappropriate because these data do not represent all parts of a whole.1.30This distribution is right-skewed, with the center around two servings and avariability of zero to eight servings. There are no outliers. About 12% (9 out of 74)consumed six or more servings, and about 35% (26 out of 74) ate fewer than twoservings (zero or one serving).1.31 (a)Ignoring the four lower outliers, the distribution is roughly symmetric, iscentered at a score of 111, and has a range of 86 to 136.(b)62 of the 78 scores aremore than 100. This is 79.5%.1.32 (a)The distribution is slightly left-skewed (some might call it almostsymmetric).(b)The center is somewhere between 0% and 2.5%.(c)The smallestvalue is somewhere between –12.5% and –10%, and the largest value is between12.5% and 15%.(d)There are about 140 negative returns, although your estimatecould differ. This corresponds to about 38%.1.33(1.)“Are you female or male?” is Histogram (c). There are two outcomespossible, and the difference in frequencies is likely to be smaller than the right-handed/left-handed difference in part (2).(2.) “Are you right-handed or left-handed?” is Histogram (b), since there are more right-handed people than left-handed people, and the difference is likely larger than the sex difference in part (1).(3.)“What is your height in inches?” is Histogram (d). Height distribution is likely tobe symmetric.(4.)“How many minutes do you study on a typical weeknight?” isHistogram (a). The variable takes on more than two values, and time spent studyingmay well be a right-skewed distribution, with most students spending less timestudying, but some students studying a lot.

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1.34 (a)A histogram is provided.(b)This is an extremely right-skewed distribution. Ratios greater than 1 correspondto an oil with more omega-3 than omega-6. This accounts for 7 of the 30 oils, or23.3%. Most food oils aren’t this healthy.(c)Of the 7 healthier food oils, 5 comefrom types of fish. Furthermore, all of the fish oils in the list have ratios higher than1. Clearly, fish oils provide a healthier ratio of omega-3 to omega-6 acids.1.35 (a)States vary in population, so you would expect more nurses in Californiathan in Wyoming, for example. Nurses per 100,000 provides a better measure of thenumber of nurses available to serve a state’s population.(b)A stemplot is provided.Round the data to the nearest ten, and use the stems for hundreds and the leaves fortens. The distribution is slightly left-skewed, with a center around 900 and a rangefrom 590 to 1480 nurses per 100,000. The observation with 1480 nurses is anoutlier. This corresponds to Washington D.C.; many people live in statessurrounding D.C. but commute to D.C. to health care.StemLeaf148130126110610012223459990011134555788001133556668724661134788959(c)Splitting the stems would be useful, because it would better allow you to see thevariability between the large number of states with between 800 and 1100 nursesper 100,000.65432102520151050RatioFrequencyFood Oils Ratio of Omega-3 to Omega-6

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1.36 (a)Because the countries have varying populations, comparing them by deathsper 1000 children is easier than by total number of children.(b)The histogram isprovided. The distribution is right-skewed, with a center around 20 deaths per 1000children. The range is from just above 0 to 160. Angola may be considered anoutlier, with a death rate of about 160.1.37The stemplot (after rounding to the nearest thousand) is shown. The shape ofthe distribution is roughly symmetric (it might be called left-skewed if we ignore thehigh outlier); with this scaling, 245 seems to be a high outlier. The center is about171 (the 12th observation). The data range from about 91 to about 245.StemLeaf2462322212012441921822170223991668151413121110996303257

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1.38 (a)A negative value means that the virtual operation took longer after thefour-week program than it took before the program.(b)The stemplot is provided.TreatmentControl-08122-0130233448887760556778999943332119154421238233(c)The center for the treatment group is about 130 seconds; for the control group,the center is about 60 seconds. It appears that the treatment group had largerdifferences, so had greater improvement.1.39A time plot of fur seal pups. The decline in population is not seen in thestemplot made in Exercise 1.37.

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1.40(a)Rates are appropriate (rather than numbers of accidents) because thegroup sizes are different. If marijuana did not increase with the rate of accidents,then you would still have more accidents (by count) in the largest groups.(b)Therates were computed as accidents / (number of drivers) in each group; a bar graphis given. While we cannot conclude that marijuana use causes accidents, it iscertainly associated with a greater accident rate. Perhaps the “risk taking” aspectmentioned might also be an explanation.51 + times11-50 times1-10 timesNever0.350.300.250.200.150.100.050.00Marijuana Use per YearAccident Rate per DriverMarijuana Use and Accidents in New Zealand

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1.41(a)A bar graph is provided. Three separate bar graphs could also have beenproduced.(b)All countries spend much more time on either a desktop or a smartphone app.The U.S. uses smartphone apps more than desktops, which is not true for Canadaand the U.K.(c)A pie chart can be constructed because within each country, the fivecategories listed cover all possible choices of access method, with the sum of thepercents being 100. Comparing the distributions across country is easier with theside-by-side bar graph because the bars are grouped by access method.

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