Solution Manual for Statistical Reasoning for Everyday Life, 5th Edition

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SOLUTIONSMANUALSTATISTICALREASONINGFOREVERYDAYLIFEFIFTHEDITIONJeffrey BennettUniversity of Colorado at BoulderWilliam L. BriggsUniversity of Colorado at DenverMario F. TriolaDutchess Community College

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iiiContentsChapter 1Speaking of Statistics..................................................................................................................1Chapter 2Measurement in Statistics.........................................................................................................9Chapter 3Visual Displays of Data..........................................................................................................17Chapter 4Describing Data..........................................................................................................................27Chapter 5A Normal World.........................................................................................................................37Chapter 6Probability in Statistics...........................................................................................................45Chapter 7Correlation and Causality......................................................................................................53Chapter 8Inferences from Samples to Populations........................................................................61Chapter 9Hypothesis Testing....................................................................................................................67Chapter 10tTests, Two-Way Tables, and ANOVA......................................................................73

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1CHAPTER 1Section 1.1Statistical Literacy and Critical Thinking1The two meanings are: (1) statistics is thescienceof collecting,organizing, and interpreting data; and (2) statistics are thedata(numbersor other pieces of information) that describe or summarize somecharacteristic from a sample. Note that for the first meaning, the word“statistics” is singular and for the second it is plural.2Apopulationis the complete set of people or things being studied, while asampleis a subset of a population. In other words, the sample is only apart of the complete population. Apopulation parameteris a characteristicof a population. Asample statisticis a characteristic of a sample found byconsolidating or summarizing raw data.Raw dataare all measurements orobservations collected. It is usually impractical to directly measurepopulation parameters for large populations, so we usually infer likelyvalues of the population parameters from the measured sample statistics.3The margin of error is used to describe the range of values in a confidenceinterval. We add and subtract the margin of error from a sample statistic tofind the confidence interval, or the range of values that is likely tocontain some population parameter. The confidence interval is used toestimate the population parameter, and the confidence level (e.g. 95%) tellsus how confident we should be that the population parameter lies within thequoted range.4The basic steps, summarized in Figure 1.1, are: (1) identify the goals; (2)choose a representative sample from the population; (3) collect raw datafrom the sample and summarize them with sample statistics; (4) use thesample statistics to make inferences about the population; (5) drawconclusions from your results. Students should come up with their ownexample.5This statement does not make sense. The statement is drawing a conclusionabout all American adults, which means it is identifying the exact value ofa population parameter. But the pollster only surveyed a sample of 1009adults, so it is not possible to know with certainty the value of thepopulation parameter.6This statement does make sense. The margin of error suggests a (presumably95%) confidence interval from 52% to 58%. However, there is always somechance that the actual population proportion is outside the confidenceinterval, and in this case it would not need to be far outside for thecandidate to lose. Moreover, the poll was taken 2 months before theelection, and voters may change their minds by election time.7This statement does not make sense. A margin of error of zero would implythat there is no uncertainty in a survey result, and that could happen onlyif the entire population was surveyed, rather than just a sample.8This statement does not make sense.The confidence interval tells us thatwe can have 95% confidence that the values from 55% to 60% contain thepopulation parameter, but we cannot be absolutely certain that the truepopulation parameter isn’t significantly lower or higher.9This statement does not make sense.Inferences about one population (males)do not necessarily apply to a different population (females).10This statement does make sense.The purpose of statistics is to help withdecision making, and if the survey was conducted well, it is possible todraw conclusions with high confidence from a survey of a 1000-person sample.If the survey results indicate that most people like the song, then it makessense to promote it, even though there is no guarantee that the promotionwill be successful.

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2CHAPTER1, SPEAKING OF STATISTICSConcepts and Applications11Sample: the 1018 adults selected. Population: the complete set of alladults (presumably in the United States). Sample statistic: 22%. Thevalue of the population parameter is not known, but it is thepercentage of all adults (presumably in the United States) who smokedcigarettes in the past week.12Sample: the 186 babies selected. Population: the complete set of allbabies. Sample statistic: 3103 g. The value of the populationparameter is not known, but it is the average (mean) birth weight ofall babies.13Sample: the 47 subjects treated with Garlicin. Population: thecomplete set of all adults. Sample statistic: 3.2 mg/dL. The value ofthe population parameter is not known, but it is the average (mean)change in LDL cholesterol.14Sample: the 150 senior executives who were surveyed. Population: thecomplete set of all senior executives. Sample statistic: 47%. Thevalue of the population parameter is not known, but it is thepercentage of all senior executives who say that the most common jobinterview mistake is to have little or no knowledge of the companywhere the applicant is being interviewed.15The range of values likely to contain the true value of the populationparameter is from 77% - 2% to 77% + 2% or from 75% to 79%.16The range of values likely to contain the true value of the populationparameter is from 85% - 1% to 85% + 1% or from 84% to 86%.17The range of values likely to contain the true value of the populationparameter is from 96% – 3% to 96% + 3% or from 93% to 99%.18The range of values likely to contain the true value of the populationparameter (mean body temperature) is 98.2º F – 0.1º F to 98.2º F +0.1º F or from 98.1º F to 98.3º F degrees.19The range of values likely to contain the true value of the populationparameter is from 57% – 4% to 57% + 4% or from 53% to 61%.20The range of values likely to contain the true value of the populationparameter is from 0.032% – 0.006% to 0.032% + 0.006% or from 0.026% to0.038%.21Based on the survey, the actual percentage of voters is expected to bebetween 67% and 73%, which does not include the 61% value from actualvoting records. If the survey was conducted well, then it is unlikelythat its result would be so different from the actual voter turnout,implying either that respondents intentionally lied to appearfavorable to the pollsters or that their memories may have beenfaulty.22It appears that the men who were surveyed may have been influenced bythe gender of the interviewer.When they were interviewed by women,they may have been more inclined to respond in a way that they thoughtwas more favorable to the female interviewers.23Yes, we can safely conclude that fewer than half of all students saythey are tired on most days. Based on the confidence interval andmargin of error, it is likely that the actual population parameter isfairly close to the 39% sample statistic, and very unlikely that thetrue value could be above 50%.24No, the results do not contradict Mendel’s theory. Using the margin oferror, it appears that the percentage of yellow peas is likely to bebetween 22% and 30%, and that range of values includes Mendel’sclaimed value of 25%, so the results do not contradict his theory.

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SECTION 1.1, WHAT IS/ARE STATISTICS?325a)Goal: determine the percentage of employees who would like to havetheir boss’s job. Population: the complete set of all employees.Population parameter: the percentage of all employees who would liketo have their boss’s job.b)Sample: the 144 employees selected for the survey. Raw data:individual responses to the question. Sample statistic: 21%.c)The range of values likely to contain the population parameter is from21% - 7% to 21% + % (or from 14% to 28%).26a)Goal: determine the percentage of older adults (aged 57 to 85 years)who use at least one prescription drug. Population: the complete setof all older adults. Population parameter: the percentage of all olderadults who use at least one prescription drug.b)Sample: the 3005 older adults selected for the survey. Raw data:individual responses to the question. Sample statistic: 82%.c)The range of values likely to contain the population parameter is from82% - 2% to 82% + 2% (or from 80% to 84%).27a)Goal: determine the percentage of adults who say that they areunderpaid. Population: the complete set of all adults. Populationparameter: the percentage of all adults who say that they areunderpaid.b)Sample: the 557 adults randomly selected and surveyed. Raw data:individual responses to the survey question. Sample statistic: 51%.c)The range of values likely to contain the population parameter is 51%- 4% to 51% + 4% (or from 47% to 55%).28a)Goal: determine the percentage of human resource professionals who saythat piercings or tattoos are big grooming red flags. Population: thecomplete set of all human resource professionals. Populationparameter: the percentage of all human resource professionals who saythat piercings or tattoos are big grooming red flags.b)Sample: the 514 human resource professionals selected for the survey.Raw data: individual responses to the question. Sample statistic: 46%.c)The range of values likely to contain the population parameter is 46%- 4% to 46% + 4% (or from 42% to 50%).29Step 1:Goal: identify the percentage of all drivers who text while theyare driving.Step 2:Choose a representative sample of drivers.Step 3:Somehow collect data on whether the drivers in the sample textwhile driving. Find the percentage who do.Step 4:Use the sample statistic to make an inference about thepercentage of all drivers who text while they are driving.Step 5:Based on the likely value of the population parameter, form aconclusion about the percentage of drivers who text while theyare driving.30Step 1:Goal: identify the average (mean) FICO score of all adults inthe United States.Step 2:Choose a sample of adult consumers.Step 3:Obtain the FICO scores of the selected adults. For this sample,find the average FICO score.Step 4:Use the sample statistic to make an inference about the averageFICO score of all adults in the United States.Step 5:Based on the likely value of the population parameter, form aconclusion about the average FICO score of all adults in theUnited States.31Step 1:Goal: identify the average (mean) weight of all commercialairline passengers.Step 2:Choose a sample of airline passengers.Step 3:Weigh each selected airline passenger, then find the average ofthose weights.

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4CHAPTER1, SPEAKING OF STATISTICSStep 4:Use the sample statistic to make an inference about theaverage weight of all airline passengers.Step 5:Based on the likely value of the population parameter, forma conclusion about the average weight of all airlinepassengers.32Step 1:Goal: identify the average (mean) length of time thatpacemaker batteries last before failure.Step 2:Choose a sample of pacemaker batteries.Step 3:Record the length of time that each battery in the samplelasts before failure. Find the average of those times.Step 4:Use the sample statistic to make an inference about theaverage length of time that all pacemaker batteries lastbefore failure.Step 5:Based on the likely value of the population parameter, forma conclusion about the average length of time that allpacemaker batteries last before failure.Section 1.2Statistical Literacy and Critical Thinking1Acensusis a collection of data from every member of a population, but asampleis a collection of data from only part of a population.2Arepresentative sampleis a sample in which the relevant characteristics ofthe sample members are generally the same as the characteristics of thepopulation. It is critically important to collect a sample that isrepresentative of the population for which you intend to make inferencesabout. Failure to obtain a representative sample is a major contributor tomisleading statistics.3Abiased sampleis a sample that somehow tends to favor certain results.Because a biased sample is not representative of the population, resultsobtained from a biased sample are likely to be misleading. Preventing biasis one of the greatest challenges in statistical research.4The five common sampling methods described in the text are:Simple random sampling: A sample of items is collected in such a waythat every sample of the same size has an equal chance of beingselected.Systematic sampling: A simple system is used to choose the sample,such as selecting every 10th or every 50th member of the population.Convenience sampling: A sample is collected that happens to beconvenient to select.Cluster sampling: The population is first divided into groups, orclusters, and some of these clusters are selected at random. Thesample is collected by choosingallthe members within each of theselected clusters.Stratified sampling: This method is used when we are concerned aboutdifferences among subgroups, orstrata, within a population. First, weidentify the strata and divide the population based on the strata. Arandom sample within each stratum is collected. The total sampleconsists of all the samples from the individual strata.5This statement does not make sense because it is not possible or practicalto survey every undergraduate statistics student, as would be required for acensus.6This statement does make sense. Even though the sample is a conveniencesample, there is no reason to think that students in a statistics classwould differ in any fundamental way from the general population of allstudents at the school in terms of handedness.

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SECTION 1.3, TYPES OF STATISTICAL STUDIES57This statement does make sense. The gender makeup of the sample shouldreflect the gender makeup of the movie-going population. While thatpopulation might not have precisely equal proportions of males and females,it certainly is not so male-dominated as this sample, so the study used abiased sample.8This statement does make sense. The procedure described does result in asimple random sample, and it is a procedure that is commonly used.Concepts and Applications9A census is practical. Even though NFL team rosters include about 1700players, it is easy to find their weights on the Internet.10A census is not practical because the number of high school football playersin California is too large and their weights are not readily available.11A census is not practical. The number of statistics students in the UnitedStates is too large (hundreds of thousands), and it would probably bedifficult to find their ages.12A census is practical. The number of members of Congress is not large (535),and their annual salaries are available on the Internet.13Sample: the 1002 surveyed subjects. Population: all adults. Sampling method:simple random sampling. The sample is likely to be representative of thepopulation.14Sample: the 4500 mailed responses from women. Population: all women.Sampling method: convenience sampling. The sample is not likely to berepresentative of the population.15Sample: the 47 responses from the website. Population: all adult Americans.Sampling method: convenience sampling. Because the sample is very small andis limited to Internet users, it is not likely to be representative of thepopulation.16Sample: the 1,059 selected adults. Population: the complete set of alladults. Sampling method: simple random sampling. Because the sample isfairly large and was obtained by a reputable firm, it is likely to berepresentative of the population.17Sample 3 is the most representative, because the list is a random samplethat is not likely to be biased. Sample 1 is a convenience sample limited toreaders of the newspaper and is therefore likely to be biased. Sample 2 islikely to be biased because it is limited to the geographic region ofAnchorage. Sample 4 is biased because it includes only car owners and doesnot include those who cannot afford a car or choose not to own a car.18Sample 4 is the most representative and is a good use of systematicsampling. Sample 1 is biased because it consists of people from onegeographic region located at the extreme southern part of the state. Sample2 is biased because it consists of people from one specific geographic urbanregion. Sample 3 is likely to be biased because it is a self-selectedsample.19There is no bias. The U.S. Department of Labor and its employees havenothing to gain by distorting the results, and they typically use very soundsampling methods.20There is no bias. Because the magazine does not accept free products or runadvertisements, it is not influenced by the manufacturers of the cars thatit reviews.21Yes, there is a possibility of bias. The university scientists receivefunding from Monsanto, so they might be inclined to please the company inthe hope of getting further funding in the future. Thus, there may be aninclination to provide favorable results. To determine whether this bias isa problem, you would need to explore the methods and conclusions verycarefully.

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6CHAPTER1, SPEAKING OF STATISTICS22Yes, there is a possibility of bias. Because the physicians receive fundingfrom the pharmaceutical company, they might be more inclined to providefavorable results so that they can get additional funding in the future.(The magazine now requires that all such physician authors disclose fundingsources, and those disclosures are included in the articles.)23The sample is a simple random sample that is likely to be representativebecause there is no bias in the selection process.24The sample is systematic and is likely to be representative because there isno inherent bias in the way that it was selected.25The sample is a cluster sample. It is likely to be representative, althoughthe exact method of selecting the polling stations could affect whether thesample is biased.26The sample is stratified. It is likely to be representative because it hasabout the same proportion of males and females as is found in thepopulation.27The sample is a convenience sample. It is likely to be biased, because itconsists of family members likely to have similar physical characteristicsand exercise habits.28The sample is a cluster sample. It is likely to be biased for severalreasons. The servers are not likely to give accurate responses. Also, thesmall number of restaurants could easily result in a sample that is notrepresentative.29The sample is a stratified sample. It is likely to be biased because peoplefrom those age groups are not evenly distributed throughout the population.However, the results could be weighted to reflect the age distribution ofthe population.30The sample is a convenience sample. The sample is likely to be biasedbecause the customers are all shopping at one upscale store, so they notlikely to be representative of all consumers.31The sample is a systematic sample. The sample is likely to be representativeof students at the college, but not representative of all college studentsin the United States.32The sample is a simple random sample. Because it is a simple random sampleand the sample size is fairly large, it is likely to be representative.33The sample is a stratified sample. It is likely to be biased because thepopulation does not have equal numbers of people in each of the 50 states.However, the results could be weighted to reflect the actual distribution ofthe population.34The sample is a cluster sample. It is likely to be representative ofstudents at the college but not representative of all college students inthe United States.35The sample is a convenience sample. It is likely to be biased because it isa self-selected sample and consists of those with strong feelings about thetopic.36The sample is a simple random sample. Because it is a simple random sample,it is likely to be representative, although a larger sample size would bebetter.37The sampling plan results in a simple random sample, which is likely to berepresentative.38The sample is a systematic sample. The sample is likely to berepresentative, unless there are special factors, such as a manufacturingprocess that somehow systematically results in defective items.39a.Stratified sampling would require that samples be obtained from everyone of the 3000 rice farms, and that would be an overwhelmingly largeproject.b.Cluster sampling would require that all of the rice be tested atrandomly selected farms.

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SECTION 1.3, TYPES OF STATISTICAL STUDIES7c.First, select a random sample of farms. Next, at each farm, randomlyselect a sample of rice to be tested.40Simple random sampling may be adequate. Better, however, would be stratifiedsampling with the different ethnic groups as the strata, since there may bedifferences in blood type distribution among these groups.41A stratified sample in which you choose a few parents at each school wouldbe effective.42a.A serious manufacturing problem could potentially be missed. As oneexample, if the end of a production run is affected by worn machinery,systematic sampling might be too slow to allow for recognition of theproblem.b.A potential problem of a simple random sample of only 5 altimeters isthat it is probably too small to represent the population.Section 1.3Statistical Literacy and Critical Thinking1Avariableis any item or quantity that can vary or take on differentvalues.Thevariables of interestin a statistical study are the items orquantities that the study seeks to measure. When cause and effect may beinvolved, anexplanatory variableis a variable that may explain or causethe effect, while aresponse variableis a variable that responds to changesin the explanatory variable.2Confoundingis the mixing of effects from different factors so that wecannot determine the effects from the specific factors being studied. Ifmales are given the treatment and females are given placebos, we would notknow whether effects are due to the treatment or the gender of theparticipant.3Aplacebois physically similar to a treatment, but it lacks any activeingredients, so it should not by itself produce any effects. Use of aplacebo is important so that results from subjects given the real treatmentcan be compared with results from subjects given the placebo.4Blindingis the practice whereby participants and/or experimenters do notknow who belongs to the treatment group and who belongs to the controlgroup. It is important to use blinding for participants so that they are notaffected by the knowledge that they are receiving the real treatment, and itis important to use it for experimenters so that they can evaluate resultsobjectively instead of being influenced by knowledge about who is gettingthe real treatment.5This statement does not make sense. The subjects who exercise obviously knowthat they are exercising. Those who evaluate results should not know whethera subject is in the treatment group of those exercising or a control groupof those not exercising. In this case, a single-blind experiment ispractical, but a double-blind experiment is not.6This statement does not make sense. The variable of interest in this studyis the durability of paints in hot weather, and the cost of the paint is notrelevant.7This statement does not make sense. As described, this experiment lacks acontrol group (e.g., a group that does not do the breathing exercises) andalso is subject to experimenter effects in which the psychologist maysomehow influence the responses of his subjects (for example, through facialexpression, tone of voice, or attitude).8This statement does make sense. It would be unethical to conduct anexperiment in which some passengers were told to drive cars with air bagsand others to drive cars without them, so a retrospective study that usespast data from accidents is the only legitimate way to investigate thisissue.

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8CHAPTER1, SPEAKING OF STATISTICSConcepts and Applications9This is an observational study because the TV viewers are being measured,but they are not treated.10This is an experiment because the samples of glass are treated.11This is an experiment. The treatment group consists of those treated withmagnets. The control group consists of those given the non-magnetic devices.12This is an observational study because the subjects were tested, but theywere not given any treatment.13This is an observational study. The subjects were tested, but they were notgiven any treatment.14This is a retrospective observational study comparing those who were textingand those who were not.15This is an experiment because the subjects were given a treatment. Thetreatment group consists of the 945 couples given the XSORT treatment. Thecontrol group consists of others not given any treatment.16This is an observational study since no treatment was given.17This is an experiment. The treatment group consists of the geneticallymodified corn, and the control group consists of corn not geneticallymodified.18This is an observational study because the subjects were surveyed, but theywere not given any treatment.19This is a meta-analysis in which all of the individual studies areobservational.20This is meta-analysis in which all of the individual studies areobservational.21Confounding is likely to occur.If there are differences in tree growth inthe two groups, it will be impossible to tell if those differences are dueto the treatment (fertilizer or irrigation) or to the type of region (moistor dry).This confounding can be avoided by using blocks of fertilizedtrees in both regions and blocks of irrigated trees in both regions.22Confounding is not likely to occur. Because every possible combination ofsite and treatment was used, it becomes possible to identify the effects ofthe site and the effects of the treatment. This was a well-plannedexperiment.23Confounding is likely to occur. If there are differences in the amounts ofgasoline consumed, there would be no way to know whether those differencesare due to the octane rating of the gasoline or the type of vehicle.Confounding can be avoided by using 87 octane gasoline in half of the vansand half of the sport utility vehicles and 91 octane gasoline in the rest ofthe vehicles. Even better would be conducting an experiment in whichidentical vehicles are driven under the same conditions (speed, distance,etc.) with the different gasolines.24Confounding is not likely. Confounding would have been possible if thecategorization of the offspring peas had been subjective, but that was notthe case.25Confounding is not likely to occur. Evaluators did not affect how the moneywas used and applied no subjective judgment in identifying how it was used.Confounding might have occurred if the subjects were informed of the purposeof the study before they made their choice, but they were not told.26Confounding is possible because the effects of the treatment may be mixedwith the effects of the physicians’ knowledge on their judgments. It wouldbe better to use blinding so that the physicians do not know who is giventhe treatment and who is given the placebo.

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SECTION 1.4, SHOULD YOU BELIEVE A STATISTICAL STUDY?927In this case, the tennis balls play the role of placebos. Confounding canoccur because of a placebo effect and/or an experimenter effect, because itwill be obvious to both subjects and experimenters whether they are liftingheavy weights. It would be better to use the heavy weights and the tennisballs with the same subjects at different times, to see if the differentregimens affect blood pressure.28Confounding is very possible. It is not possible to disguise the car modelsand they have different reputations and very different prices that couldaffect the evaluations made by the driver.29The control group consists of those who do not listen to Beethoven’s music,and the treatment group consists of those who do listen to it. This shouldbe a single-blind experiment. Subjects know whether they are listening toBeethoven, but blinding should be used so that those who measureintelligence are not influenced by their knowledge about whether there wasexposure to Beethoven’s music. The blinding could be accomplished byassigning code numbers to subjects, with only the researchers knowing whichcode numbers belonged to the treatment group and which belonged to thecontrol group.30This should be a double-blind experiment with a control group consisting ofsubjects given placebos and a treatment group consisting of those treatedwith Echinacea. Participants should be randomly assigned to the two groups.31The control group consists of smartphones with the current battery, and thetreatment group consists of smartphones with the new battery. Blinding isnot necessary for the smartphones because they are not that smart, and it isprobably unnecessary for the researchers because the longevity of thebatteries will likely be measured with objective tools.32It is sufficient to use the three different groups of homes with aluminumsiding, vinyl siding, and wood siding. It isn’t necessary to identify one ofthe groups as a control group. Blinding is not necessary for the houses, andit is unnecessary for the researchers if the longevity is measured withobjective tools. Blinding would be difficult to implement because whether ahome has aluminum siding or vinyl siding or wood siding would be obvious tothose who evaluate the results.Section 1.4Statistical Literacy and Critical Thinking1The eight guidelines are as follows:1. Get a big picture view of the study.2. Consider the source.3. Look for bias in the sample.4. Look for problems in defining or measuring the variables of interest.5. Beware of confounding variables.6. Consider the setting and wording in surveys.7. Check that results are presented fairly.8. Consider the conclusions.2Peer review is a process in which experts in a field evaluate a researchreport before the report is published. It is useful in lending credibilityto the research because it implies that other experts agree that it wascarried out properly.3Selection bias occurs when researchers select their sample in a way thattends to make it unrepresentative of the population, and participation biasoccurs when the participants themselves choose to be included in the study.4When participants select themselves for a survey, those with strong opinionsabout the topic being surveyed are more likely to participate, and thisgroup is typically not representative of the general population.

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10CHAPTER 1, SPEAKING OF STATISTICS5This statement does not make sense.A survey involving a large sample couldgive very poor results if the sample is chosen with a poor sampling method(such as self-selection), while a smaller sample could produce much betterresults if a sound sampling method is used (such as simple random sampling).6This statement does not make sense. If a sample is biased, it is biased nomatter how large it is.7This statement does not make sense. The clinical trial might show that thetreatmentresults in lower blood pressure levels, but if the amount of thedecrease is very small, it is possible that the treatment does not havepractical significance.8This statement does not make sense. It generally isn’t possible to controlfor all confounding variables, since you might not even know that some ofthem exist.Concepts and Applications9The survey was funded by a source that can benefit through increased salesfostered by the survey results, so there is a potential for bias in thesurvey. Guideline 2 is most relevant.10“Good” is not well defined and is difficult to measure. Guideline 4 is mostrelevant.11The weather and rainfall conditions in California are different from thosein Hawaii. It is impossible to determine whether differences are due to thesystems or the weather and rainfall conditions. Guideline 5 is mostrelevant.12The sample of male college students is a biased sample, so the effectivenessof the treatment does not necessarily apply to subjects in the generalpopulation of American adults. Guideline 3 is most relevant.13Because the researchers received funding from the pharmaceutical company,there is clearly potential for distorting the results so that they willplease the pharmaceutical company. Guideline 2 (source) is most relevant14The results are not being reported fairly. Guideline 7 is most relevant.15The question is too vague and allows for different interpretations of howmuch violence is too much. The question does not address a variable that canbe measured in a meaningful way. Guideline 4 is most relevant.16The use of the word “wasteful” is likely to encourage negative responses, sothe wording is not appropriate. Guideline 6 is most relevant.17Because much of the funding was provided by Mars and the ChocolateManufacturers Association, the researchers may have been inclined to providefavorable results. The bias could have been avoided if the researchers werenot paid by the chocolate manufacturers. If that was the only way theresearch could be done, then the researchers should institute procedures toensure that they publish all results, including negative ones.18The sample is self-selected and involves a small proportion of thepopulation of women, so the responses were more likely to come from thosewith strong feelings about the issues. A better sampling procedure, such asinterviews with 4,500 randomly chosen women, should have been used.19The wording of the question was biased to strengthen opposition against aparticular candidate. The opinion poll is likely to be a “push poll”financed by supporters of another candidate, rather than a legitimate poll.A better survey would pose questions devoid of such bias.20A list of property owners is clearly biased toward those who can afford toown property. Also, a mail survey will result in a self-selected sample. Abetter sampling method, such as the simple random sampling used by mostpolling companies, should be used.

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CHAPTER 1 REVIEW EXERCISES1121The word “wrong” in the first question could be misleading. Some peoplemight believe that abortion is wrong, but still favor choice. The secondquestion could also be confusing, as some people might think that “advice ofher doctor” means that the woman’s life is in danger, which could altertheir opinion about abortion in this situation. Groups opposed to abortionwould be likely to cite the results of the first question, while groupsfavoring choice would be more likely to cite the results of the secondquestion.22The first question refers to “government programs,” which many peopleconsider to be generally wasteful. The second question lists specificprograms that are very popular. Groups favoring tax cuts would be likely tocite the results of the first question, and groups opposed to tax cuts wouldbe more likely to cite the results of the second question.23The headline refers to drugs whereas the story specifically cites “drug use,drinking, or smoking.” Because “drugs” are generally considered to consistof drugs other than cigarettes or alcohol, the headline is very misleading.24The story does not include the margin of error. With a sample size of 500,the margin of error is around 4 percentage points, so the likely range for asatisfying sex life is 78% to 86%, and the likely range for job satisfactionis 75% to 83%. Because these ranges overlap, it is quite possible that theheadline is incorrect.25No information is given about the sample size, margin of error, or howsubjects were selected and measured. The reported “percentage” of 1 in 4 isnot very precise, and it is not really a percentage.26The report appears to be making a statement about the quality of restaurantsin New York City (the “Big Apple”), but much information is missing. Whatabout restaurants with ratings of 30 or 28? What criteria were used for theratings? Who actually did the rating?27No information is given to justify the statement “More companies try to beton forecasting weather.” If only the four cited companies make up theincrease, it is relatively insignificant.28The headline suggests that China has been thrown off balance, implying thatsome change is having a dramatic effect, but no information is given aboutany such change.Chapter 1 Review Exercises1a)The range of values likely to contain the proportion of all adultswith tattoos is from 82% - 1% to 82% + 1% or from 81% to 83%.b)The population consists of all adults aged 57 through 85 years.c)It is an observational study because the subjects were not treated ormodified in any way. The variable of interest is whether the subjectuses at least one prescription medication. For this survey, thatvariable has two values: yes or no.d)The reported value is a sample statistic because it is based on thesample of 3005 adults aged 57 through 85 years, not the population ofall adults in that age bracket.e)No, because that method would produce a self-selected sample and alikely participation bias.f)(i) Systematic sampling; (ii) simple random sampling; (iii) stratifiedsampling; (iv) convenience sampling; (v) cluster sampling2a)It is a sample chosen in such a way that every sample of the same sizehas the same chance of being selected.b)No, because not every sample of 2007 people has the same chance ofbeing selected. For example, it is impossible to select a sampleconsisting of 2007 people in the same primary sampling unit. Insteadof being a simple random sample, this is a stratified sample.

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12CHAPTER 1, SPEAKING OF STATISTICSc)Repeat the process of randomly selecting a primary sampling unit fromone of the 2007 that are available, then randomly selecting one of itsmembers. If the same adult is selected more than once, ignore thesecond and any subsequent repeat selections.3a)No. There is no information about the occurrence of rhinovirusinfections among people who do not use Echinacea. Also, the subjectswho did not get rhinovirus infections may have been influenced byfactors other than the Echinacea treatment.b)It appears that Echinacea users have about the same rate of rhinovirusinfections as those given a placebo, so Echinacea use does not appearto have an effect on rhinovirus infections.c)With blinding, the subjects do not know whether they are gettingEchinacea or a placebo, and with double blinding, those who evaluatethe results also do not know.d)This is an experiment because subjects are given a treatment.e)An experimenter effect occurs if the experimenter somehow influencessubjects through such factors as facial expression, tone of voice, orattitude. It can be avoided through the use of blinding.4a)Because the word “welfare” has negative connotations, the secondquestion should be used.b)The first question, because it is more likely to elicit negativeresponses.c)This is largely a subjective judgment. Some professional pollsters areopposed to all such questions that are deliberately biased, but othersbelieve that such questions can be used. An important consideration isthat the wording of survey questions can modify how people think, andsuch modification should not occur without their awareness oragreement.Chapter 1 Quiz1Population: all Internet users. Sample: the 500 Internet users who weresurveyed.2The method used is stratified sampling.3The value of 5% is a sample statistic.4(a) The results found for the sample are similar to those we would find forthe entire population.5The survey results are a sample.6It is an experiment.7(b)This trial is double-blind.8(a) The purpose of the placebo is to prevent participants from knowingwhether they belong to the treatment group or the control group.9(c)It means pulse rates were lowered among some of those in the placebogroup.10(b) There is a danger of confounding.11The range of values likely to contain the true value of the populationparameter is from 51% - 3% to 51% + 3% or from 48% to 54%.12No, we cannot conclude that the majority of people are most annoyed by theuse of “whatever” in conversations because the population parameter theconfidence interval spans from 48% to 54%.The true value of the populationparameter could be less than 50% (less than majority).13(b) The variable of interest in this study is the weights of dolphins.14(c) People who use sunscreen are more likely to spend time in the sun.15(b) Whenever we do a statistical study using a sample from a population,there is always a small chance, even when everything is done correctly to tryto ensure that the sample is representative of the population, that theconclusions drawn about the population based on the sample results are notcorrect.

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13CHAPTER 2Section 2.1Statistical Literacy and Critical Thinking1Qualitative data consist of values that can be placed in different non-numerical categories, (such as male, female, or Democrat, Republican),whereas quantitative data consist of values representing counts ormeasurements.2Discrete data have only particular values, such as integers, whilecontinuous data can take on any value. Counts of people are an example ofdiscrete data, since they can be only whole numbers (integers); weights ofpeople are continuous data, since they can take on any value.3Data at the nominal level of measurement are described solely by names,labels, or categories. The ordinal level applies to qualitative data thatcan be arranged in some order (such as low to high). The interval levelapplies to quantitative data for which intervals are meaningful, but ratiosare not. The ratio level applies to quantitative data for which bothintervals and ratios are meaningful.4Temperatures on the Fahrenheit or Celsius scales are at the interval levelof measurement because each degree of difference has a precise meaning, butthey are not at the ratio level because the zero points on these temperaturescales are arbitrary. Distances are at the ratio level because a distance ofzero has an unambiguous meaning; thus, ratios of distances are meaningful.5This statement does not make sense. Party affiliations are qualitative data,and identifying them with numbers does not change that fact. It does notmake sense to average qualitative data, as you can tell by realizing thatthe statement is claiming that the average party affiliation is halfwaybetween Republican and Independent. There’s no way to define what that mightmean.6This statement does not make sense. ZIP codes do not consistently measuredistance from the east coast or from any other reference point, so they arequalitative data.7This statement does not make sense. Temperatures on the Fahrenheit scale areat the interval, not ratio, level of measurement, so ratios like “twice as…”are not meaningful.8This statement does makes sense. Although calendar years generally representdata at the interval level of measurement (see Example 3c), the time since aparticular date, such as the beginning of a century, has a clear startingpoint and therefore represents data at the ratio level of measurement.Therefore, it is correct to say that a particular year is halfway through acentury.Concepts and Applications9Blood groups are qualitative because they don’t measure or count anything.10Pulse rates are quantitative because they consist of measurements.11Blood alcohol concentration data are quantitative because they consist ofmeasurements.12The categories of sports are qualitative because they don’t measure or countanything.13The responses “yes”, “no” or “no response” are qualitative because theydon’t measure or count anything.14Head circumferences are quantitative because they consist of measurements.15Identifications of the television shows watched are qualitative because theydon’t measure or count anything.

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