Solution Manual for Essentials of Statistics, 6th Edition

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SOLUTIONSMANUALJAMESLAPPColorado Mesa UniversityESSENTIALS OFSTATISTICSSIXTHEDITIONMario F. TriolaDutchess Community College

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CONTENTSChapter 1: Introduction To StatisticsSection 1-1: Statistical and Critical Thinking...................................................................1Section 1-2: Types of Data ...............................................................................................3Section 1-3: Collecting Sample Data................................................................................4Chapter Quick Quiz ..........................................................................................................5Review Exercises ..............................................................................................................5Cumulative Review Exercises ..........................................................................................6Chapter 2: Exploring Data with Tables and GraphsSection 2-1: Frequency Distributions for Organizing and Summarizing Data.................7Section 2-2: Histograms..................................................................................................12Section 2-3: Graphs That Enlighten and Graphs That Deceive......................................14Section 2-4: Scatterplots, Correlation, and Regression ..................................................17Chapter Quick Quiz ........................................................................................................19Review Exercises ............................................................................................................19Cumulative Review Exercises ........................................................................................21Chapter 3: Describing, Exploring, and Comparing DataSection 3-1: Measures of Center.....................................................................................23Section 3-2: Measures of Variation ................................................................................28Section 3-3: Measures of Relative Standing and Boxplots.............................................33Chapter Quick Quiz ........................................................................................................36Review Exercises ............................................................................................................37Cumulative Review Exercises ........................................................................................38Chapter 4: ProbabilitySection 4-1: Basic Concepts of Probability ....................................................................39Section 4-2: Addition Rule and Multiplication Rule ......................................................41Section 4-3: Complements, Conditional Probability, and Bayes’ Theorem...................43Section 4-4: Counting .....................................................................................................45Chapter Quick Quiz ........................................................................................................48Review Exercises ............................................................................................................48Cumulative Review Exercises ........................................................................................49Chapter 5: Discrete Probability DistributionsSection 5-1: Probability Distributions ............................................................................51Section 5-2: Binomial Probability Distributions.............................................................53Section 5-3: Poisson Probability Distributions ...............................................................56Chapter Quick Quiz ........................................................................................................58Review Exercises ............................................................................................................58Cumulative Review Exercises ........................................................................................59

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Chapter 6: Normal Probability DistributionsSection 6-1: The Standard Normal Distribution .............................................................61Section 6-2: Real Applications of Normal Distributions................................................62Section 6-3: Sampling Distributions and Estimators ......................................................66Section 6-4: The Central Limit Theorem........................................................................71Section 6-5: Assessing Normality...................................................................................73Section 6-6: Normal as Approximation to Binomial ......................................................77Chapter Quick Quiz ........................................................................................................79Review Exercises ............................................................................................................80Cumulative Review Exercises ........................................................................................81Chapter 7: Estimating Parameters and Determining Sample SizesSection 7-1: Estimating a Population Proportion............................................................83Section 7-2: Estimating a Population Mean....................................................................87Section 7-3: Estimating a Population Standard Deviation or Variance..........................91Section 7-4: Bootstrapping: Using Technology for Estimates .......................................95Chapter Quick Quiz ........................................................................................................96Review Exercises ............................................................................................................97Cumulative Review Exercises ........................................................................................98Chapter 8: Hypothesis TestingSection 8-1: Basics of Hypothesis Testing .....................................................................99Section 8-2: Testing a Claim About a Proportion.........................................................101Section 8-3: Testing a Claim About a Mean.................................................................107Section 8-4: Testing a Claim About a Standard Deviation or Variance .......................112Chapter Quick Quiz ......................................................................................................114Review Exercises ..........................................................................................................115Cumulative Review Exercises ......................................................................................116Chapter 9: Chapter 9: Inferences from Two SamplesSection 9-1: Two Proportions .......................................................................................119Section 9-2: Two Means: Independent Samples...........................................................128Section 9-3: Two Dependent Samples (Matched Pairs) ...............................................135Chapter Quick Quiz ......................................................................................................139Review Exercises ..........................................................................................................140Cumulative Review Exercises ......................................................................................141Chapter 10: Correlation and RegressionSection 10-1: Correlation..............................................................................................145Section 10-2: Regression ..............................................................................................152Section 10-3: Rank Correlation ....................................................................................165Chapter Quick Quiz ......................................................................................................166Review Exercises ..........................................................................................................166Cumulative Review Exercises ......................................................................................167

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Chapter 11: Goodness-of-Fit and Contingency TablesSection 11-1: Goodness-of-Fit......................................................................................169Section 11-2: Contingency Tables ................................................................................173Section 11-3: One-Way ANOVA .................................................................................177Chapter Quick Quiz ......................................................................................................179Review Exercises ..........................................................................................................179Cumulative Review Exercises ......................................................................................181

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Section 1-1: Statistical and Critical Thinking1Chapter 1: Introduction to StatisticsSection 1-1: Statistical and Critical Thinking1.The respondents are a voluntary response sample or a self-selected sample. Because those with strong interestsin the topic are more likely to respond, it is very possible that their responses do not reflect the opinions orbehavior of the general population.2.a. The sample consists of the 1046 adults who were surveyed. The population consists of all adults.b. When asked, respondents might be inclined to avoid the shame of the unhealthy habit of not washing theirhands, so the reported rate of 70% might well be much higher than it is in reality. It is generally better toobserve or measure human behavior than to ask subjects about it.3.Statistical significance is indicated when methods of statistics are used to reach a conclusion that a treatment iseffective, but common sense might suggest that the treatment does not make enough of a difference to justify itsuse or to be practical. Yes, it is possible for a study to have statistical significance, but not practicalsignificance.4.No. Correlation does not imply causation. The example illustrates a correlation that is clearly not the result ofany interaction or cause effect relationship between deaths in swimming pools and power generated fromnuclear power plants.5.Yes, there does appear to be a potential to create a bias.6.No, there does not appear to be a potential to create a bias.7.No, there does not appear to be a potential to create a bias.8.Yes, there does appear to be a potential to create a bias.9.The sample is a voluntary response sample and has strong potential to be flawed.10. The samples are voluntary response samples and have potential for being flawed, but this approach might benecessary due to ethical considerations involved in randomly selecting subjects and somehow imposingtreatments on them.11. The sampling method appears to be sound.12. The sampling method appears to be sound.13. With only a 1% chance of getting such results with a program that has no effect, the program appears to havestatistical significance. Also, because the average loss of 22 pounds does seem substantial, the program appearsto also have practical significance.14. Because there is a 0.3% chance of getting such results by chance, the increase in scores does appear to havestatistical significance. The typical increase of 5 points suggests that the course does have practical significance.The course does appear to be successful.15. Because there is a 19% chance of getting that many girls by chance, the method appears to lack statisticalsignificance. The result of 1020 girls in 2000 births (51% girls) is above the approximately 50% rate expectedby chance, but it does not appear to be high enough to have practical significance. Not many couples wouldbother with a procedure that raises the likelihood of a girl from 50% to 51%.16. Because there is a 25% chance of getting such results with a program that has no effect, the program does notappear to have statistical significance. Because the average increase is only 3 IQ points, the program does notappear to have practical significance.17. Yes. Each column of 8 AM and 12 AM temperatures is recorded from the same subject, so each pair ismatched.18. No. The source is from university researchers who do not appear to gain from distorting the data.19. The data can be used to address the issue of whether there is a correlation between body temperatures at8 AM and at 12 AM. Also, the data can be used to determine whether there are differences between bodytemperatures at 8 AM and at 12 AM.

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2Chapter 1: Introduction to Statistics20. Because the differences could easily occur by chance (with a 64% chance), the differences do not appear tohave statistical significance.21. No. The white blood cell counts measure a different quantity than the red blood cell counts, so their differencesare meaningless.22. The issue that can be addressed is whether there is a correlation, or association, between white blood cell countsand red blood cell counts.23. No. The National Center for Health Statistics has no reason to collect or present the data in a way that is biased.24. No. Correlation does not imply causation, so a statistical correlation between white blood cell counts and redblood cell counts should not be used to conclude that higher white blood cell counts are the cause of higher redblood cell counts.25. It is questionable that the sponsor is the Idaho Potato Commission and the favorite vegetable is potatoes.26. The sample is a voluntary response sample, so there is a good chance that the results do not reflect the largerpopulation of people who have a water preference.27. The correlation, or association, between two variables does not mean that one of the variables is the cause of theother. Correlation does not imply causation. Clearly, sour cream consumption is not directly related in any wayto motorcycle fatalities.28. The sponsor of the poll is an electronic cigarette maker, so the sponsor does have an interest in the poll results.The source is questionable.29. a. 700 adultsb. 55%30. a. 253.31 subjectsb. No. Because the result is a count of people among the 347 who were surveyed, the result must be a wholenumber.c. 253 subjectsd. 32%31. a. 559.2 respondentsb. No. Because the result is a count of respondents among the 1165 engaged or married women who weresurveyed, the result must be a whole number.c. 559 respondentsd. 8%32. a. 293.17 womenb. No. Because the result is a count of women among the 1543 who were surveyed, the result must be a wholenumber.c. 293 womend. 15%e. Interpretations of a “typical” week and what it means to “kick back and relax” might vary considerably bydifferent survey respondents. The survey might be improved by asking about behavior within “the past sevendays” instead of a “typical” week. Instead of “kick back and relax,” respondents might be surveyed aboutspecific behavior, such as reading, taking a nap, watching television, listening to music, or going for a walk.33. Because a reduction of 100% would eliminate all of the size, it is not possible to reduce the size by 100% ormore.34. In an editorial criticizing the statement, theNew York Timescorrectly interpreted the 100% improvement tomean that no baggage is being lost, which was not true.35. Because a reduction of 100% would eliminate all plaque, it is not possible to reduce it by more than 100%.

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Section 1-2: Types of Data336. If one subgroup receives a 4% raise and another subgroup receives a 4% raise, the combined group will receivea 4% raise, not an 8% raise. The percentages should not be added in this case.37. The wording of the question is biased and tends to encourage negative responses. The sample size of 20 is toosmall. Survey respondents are self-selected instead of being randomly selected by the newspaper. If 20 readersrespond, the percentages should be multiples of 5, so 87% and 13% are not possible results.38. All percentages of success should be multiples of 5. The given percentages cannot be correct.Section 1-2: Types of Data1.The population consists of all adults in the United States, and the sample is the 2276 adults who were surveyed.Because the value of 33% refers to the sample, it is a statistic.2.a. quantitativeb. categoricalc. categoricald. quantitative3.Only part (a) describes discrete data.4.a. The sample is the 1020 adults who were surveyed. The population is all adults in the United States.b. statisticc. ratiod. discrete5.statistic6.statistic7.parameter8.parameter9.statistic10. statistic11. parameter12. parameter13. continuous14. continuous15. discrete16. discrete17. discrete18. continuous19. continuous20. discrete21. ordinal22. nominal23. nominal24. ratio25. interval26. ordinal27. ordinal28. interval29. The numbers are not counts or measures of anything. They are at the nominal level of measurement, and itmakes no sense to compute the average (mean) of them.30. The digits are not counts or measures of anything. They are at the nominal level of measurement and it makesno sense to calculate their average (mean).31. The temperatures are at the interval level of measurement. Because there is no natural starting point with0 Frepresenting “no heat,” ratios such as “twice” make no sense, so it is wrong to say that it is twice as warm at theauthor’s home as it is in Auckland, New Zealand.32. The ranks are at the ordinal level of measurement. Differences between the universities cannot be determined,so there is no way to know whether the difference between Princeton and Harvard is the same as the differencebetween Yale and Columbia.33. a. Continuous, because the number of possible values is infinite and not countable.b. Discrete, because the number of possible values is finite.c. Discrete, because the number of possible values is finite.d. Discrete, because the number of possible values is infinite and countable.

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4Chapter 1: Introduction to StatisticsSection 1-3: Collecting Sample Data1.The study is an experiment because subjects were given treatments.2.The subjects in the study did not know whether they were taking a placebo or the paracetamol medication, andthose who administered the pills also did not know.3.The group sample sizes of 547, 550, and 546 are all large so that the researchers could see the effects of theparacetamol treatment.4.The sample appears to be a convenience sample. Given that the subjects were randomly assigned to the threedifferent treatment groups, it appears that the results of the study are good because they are not likely to bedistorted from bias, but we should investigate the sample groups to ensure that they are not fundamentallydifferent from the population.5.The sample appears to be a convenience sample. By e-mailing the survey to a readily available group of Internetusers, it was easy to obtain results. Although there is a real potential for getting a sample group that is notrepresentative of the population, indications of which ear is used for cell phone calls and which hand isdominant do not appear to be factors that would be distorted much by a sample bias.6.The study is an observational study because the subjects were not given any treatment.7.With 717 responses, the response rate is 14%, which does appear to be quite low. In general, a very lowresponse rate creates a serious potential for getting a biased sample that consists of those with a special interestin the topic.8.Answers vary, but the following are good possibilities.a. Obtain a printed copy of the class roster, assign consecutive numbers (integers), then use a computer torandomly generate six of those numbers.b. Select every third student leaving class until six students are chosen.c. Randomly select three males and three females.d. Randomly select a row, and then select the students in that row. (Use only the first six to meet therequirement of a sample of size six.)9.systematic10. convenience11. random12. stratified13. cluster14. random15. stratified16. systematic17. random18. cluster19. convenience20. systematic21. Observational study. The sample is a convenience sample consisting of subjects who decided themselves torespond. Such voluntary response samples have a high chance of not being representative of the largerpopulation, so the sample may well be biased. The question was posted in an electronic edition of a newspaper,so the sample is biased from the beginning.22. Experiment. The sample subjects consist of male physicians only. It would have been better to include females.Also, it would be better to include male and females who are not physicians.23. Experiment. This experiment would create anextremelydangerous and illegal situation that has a real potentialto result in injury or death. It’s difficult enough to drive in New York City while being completely sober.24. Observational study. The sample of four males and four females is too small.25. Experiment. The biased sample created by using drivers from New York City cannot be fixed by using a largersample. The larger sample will still be a biased sample that is not representative of drivers in the United States.26. Experiment. Calling the subjects and asking them to report their weights has a high risk of getting results that donot reflect the actual weights. It would have been much better to somehow measure the weights instead ofasking the subjects to report them.

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Chapter Quick Quiz527. Observational study. Respondents who have been convicted of felonies are not likely to respond honestly to thesecond question. The survey will suffer from a “social desirability bias” because subjects will tend to respond inways that will be viewed favorably by those conducting the survey.28. Observational study. The number of responses is very small, and the response rate of only 1.52% is far toosmall. With such a low response rate, there is a real possibility that the sample of respondents is biased andconsists only of those with special interests in the survey topic.29. prospective study30. retrospective study31. cross-sectional study32. prospective study33. matched pairs design34. randomized block design35. completely randomized design36. matched pairs design37. a. Not a simple random sample, but it is a random sample.b. Simple random sample and also a random sample.c. Not a simple random sample and not a random sample.Chapter Quick Quiz1.No. The numbers do not measure or count anything.2.nominal3.continuous4.quantitative data5.ratio6.statistic7.no8.observational study9.The subjects did not know whether they were getting aspirin or the placebo.10. simple random sampleReview Exercises1.The survey sponsor has the potential to gain from the results, which raises doubts about the objectivity of theresults.2.a. The sample is a voluntary response sample, so the results are questionable.b. statisticc. observational study3.Randomized: Subjects were assigned to the different groups through a process of random selection, wherebythey had the same chance of belonging to each group. Double-blind: The subjects did not know which of thethree groups they were in, and the people who evaluated results did not know either.4.No. Correlation does not imply causality.5.Only part (c) is a simple random sample.6.Yes. The two questions give the false impression that they are addressing very different issues. Most peoplewould be in favor of defending marriage, so the first question is likely to receive a substantial number of “yes”responses. The second question better describes the issue and subjects are much more likely to have variedresponses.7.a. discreteb. ratioc. The mailed responses would be a voluntary response sample, so those with strong opinions or greater interestin the topics are more likely to respond. It is very possible that the results do not reflect the true opinions of thepopulation of all full-time college students.d. stratifiede. cluster

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6Chapter 1: Introduction to Statistics8.a. If they have no fat at all, they have 100% less than any other amount with fat, so the 125% figure cannot becorrect.b. 686c. 28%9.a. interval data; systematic sampleb. nominal data; stratified samplec. ordinal data; convenience sample10. Because there is a 15% chance of getting the results by chance, those results could easily occur by chance so themethod does not appear to have statistical significance. The result of 236 girls in 450 births is a rate of 52.4%,so it is above the 50% rate expected by chance, but it does not appear to be high enough to have practicalsignificance. The procedure does not appear to have either statistical significance or practical significance.Cumulative Review Exercises1.The mean is360017004000390031003800220030003162.58grams. The weights all end with00, suggesting that all of the weights are rounded to the hundreds place, so that the last two digits are always 00.2.60.50.0156253.27217616,6which is an unusually high value.4.98.298.66.640.62106 5.221.960.2510670.036.400017005754grams7.236003162.527, 343.757grams28.22298.4-98.698.6-98.698.8-98.60.040.203-19.80.40.0006553610.11931, 381,059, 609 (or about 31, 381,060, 000)11.14678,364,164,096 (or about 78,364,164,000)12.120.30.000000531441

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Section 2-1: Frequency Distributions for Organizing and Summarizing Data7Chapter 2: Exploring Data with Tables and GraphsSection 2-1: Frequency Distributions for Organizing and Summarizing Data1.The table summarizes 50 service times. It is not possible to identify the exact values of all of the original times.2.The classes of 60–120, 120–180, …, 300–360 overlap, so it is not always clear which class we should put avalue in. For example, the value of 120 could go in the first class or the second class. The classes should bemutually exclusive.3.Time (sec)Relative Frequency60–11914%120–17944%180–23928%240–2994%300–35910%4.The sum of the relative frequencies is 125%, but it should be 100%, with a small round off error. All of therelative frequencies appear to be roughly the same, but if they are from a normal distribution, they should startlow, reach a maximum, and then decrease.5.Class width: 10Class midpoints: 24.5, 34.5, 44.5, 54.5, 64.5, 74.5, 84.5Class boundaries: 19.5, 29.5, 39.5, 49.5, 59.5, 69.5, 79.5, 89.5Number: 876.Class width: 10Class midpoints: 24.5, 34.5, 44.5, 54.5, 64.5, 74.5Class boundaries: 19.5, 29.5, 39.5, 49.5, 59.5, 69.5, 79.5Number: 877.Class width: 100Class midpoints: 49.5, 149.5, 249.5, 349.5, 449.5, 549.5, 649.5Class boundaries: –0.5, 99.5, 199.5, 299.5, 399.5, 499.5, 599.5, 699.5Number: 1538.Class width: 100Class midpoints: 149.5, 249.5, 349.5, 449.5, 549.5Class boundaries: 99.5, 199.5, 299.5, 399.5, 499.5, 599.5Number: 1479.No. The maximum frequency is in the second class instead of being near the middle, so the frequencies belowthe maximum do not mirror those above the maximum.10. Yes. The frequencies start low, reach a maximum of 36, and then decrease. The values below the maximum arevery roughly a mirror image of those above it.11.Duration (sec)Frequency125–1491150–1740175–1990200–2243225–24934250–27412

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8Chapter 2: Exploring Data with Tables and Graphs12. The intensities do not appear to have a normal distribution.Tornado F-ScaleFrequency02411622324113.Burger King LunchService Times (sec)Frequency70–10911110–14923150–1897190–2296230–2693230–269614.Burger King DinnerService Times (sec)Frequency30–69170–1096110–14926150–1897190–2293230–2696270–309115. The distribution does not appear to be a normal distribution.Wendy’s LunchService Times (sec)Frequency70–14925150–22915230–3096310–3893390–469116. The distribution does appear to be a normal distribution.Wendy’s DinnerService Times (sec)Frequency30–69470–10911110–14915150–18910190–2294230–2696

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Section 2-1: Frequency Distributions for Organizing and Summarizing Data917. Because there are disproportionately more 0s and 5s, it appears that the heights were reported instead ofmeasured. Consequently, it is likely that the results are not very accurate.Last DigitFrequency09122133415156270839118. Because there are disproportionately more 0s and 5s, it appears that the weights were reported instead ofmeasured. Consequently, it is likely that the results are not very accurate.Last DigitFrequency026112132425126170849119. The actresses appear to be younger than the actors.Age When Oscar Was WonRelative Frequency(Actresses)Relative Frequency(Actors)20 – 2933.3%1.1%30 – 3939.1%32.2%40 – 4916.1%41.4%50 – 593.4%17.2%60 – 695.7%6.9%70 – 791.1%1.1%80 – 891.1%20. There do appear to be differences, but overall they are not very substantial differences.Blood Platelet CountMalesFemales0–990.7%100–19933.3%17.0%200–29958.8%62.6%300–3996.5%19.0%400–4990%0%500–5990%1.4%600–6990.7%

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10Chapter 2: Exploring Data with Tables and Graphs21.Age (years) of Best Actress When Oscar Was WonCumulative FrequencyLess than 3029Less than 4063Less than 5077Less than 6080Less than 7085Less than 8086Less than 908722.Age (years) of Best ActorWhen Oscar Was WonCumulative FrequencyLess than 301Less than 4029Less than 5065Less than 6080Less than 7086Less than 808723. No. The highest relative frequency of 24.8% is not much higher than the others.Adverse ReactionRelative FrequencyHeadache23.6%Hypertension8.7%Upper Resp. Tract Infection24.8%Nasopharyngitis21.1%Diarrhea21.9%24. Yes, it appears that births occur on the days of the week with frequencies that are about the same.DayRelative FrequencyMonday13.0%Tuesday16.5%Wednesday18.0%Thursday14.3%Friday14.3%Saturday10.8%Sunday13.3%25. Yes, the frequency distribution appears to be a normal distribution.Systolic BloodPressure (mm Hg)Frequency80–9911100–119116120–139131140–15934160–1797180–1991

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Section 2-1: Frequency Distributions for Organizing and Summarizing Data1126. Yes, the frequency distribution appears to be a normal distribution.Diastolic BloodPressure (mm Hg)Frequency40–542755–6910770–8413385–9931100–114227. Yes, the frequency distribution appears to be a normal distribution.MagnitudeFrequency1.00–1.49191.50–1.99972.00–2.491872.50–2.991473.00–3.491003.50–3.99384.00–4.4984.50–4.99428. No, the frequency distribution does not appear to be a normal distribution.Depth (km)Frequency0.0–9.953910.0–19.94920.0–29.91030.0–39.9140.0–49.9129. An outlier can dramatically increase the number of classes.Weight (lb)With OutlierWithout Outlier200–21966220–23955240–2591212260–2793636280–2998787300–3192828320–3390340–3590360–3790380–3990400–4190420–4390440–4590460–4790480–4990500–5191

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