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Instructors Solutions Manual - Chapter 1

4. Although Statistics Canada takes great care in its data collection, errors do still occur,and data revisions are required. An interesting overview of GDP data quality forseven OECD countries is available athttp://www.oecd.org/dataoecd/20/26/34350524.pdfYou should be able to locate other information about data revisions. See also

http://www.statcan.ca/english/about/policy/infousers.htmwhich describes Statistics Canadas policy on informing users about data quality.

5. At least some of the secondary data sources listed in Section 1.1 should help you. Ifyou cannot locate any secondary data, get help from a librarian.

Develop Your Skills 1.2

6. The goal for companies is to create population data, but it is unlikely that everycustomer is captured in any CRM database. There are many examples of companiesusing CRM data. A search of the CBCA database on August 7, 2009 produced a listof 102 articles (for 2009) that contained customer relationship management as part

of their citation and indexing. For example, the publication called "Direct Marketing"regularly writes about database marketing, data mining, and web analytics. Seehttp://www.dmn.ca/index.html.

7. This is a nonstatistical sample, and could be described as a convenience sample. Therestaurant presumably has diners on nights other than Friday, and none of these couldbe selected for the sample. The owner should not rely on the sample data to describeall of the restaurant's diners, although the sample might be useful to test reaction to anew menu item, for example.

8. These are sample statistics, as they are based on sample data. It would be impossibleto collect data from all postsecondary students.

9. Follow the instructions for Example 1.2c. The random sample you get will bedifferent, but here is one example of the 10 names selected randomly.

AVERY MOORE

EMILY MCCONNELL

HARRIET COOGAN

DYLAN MILES

TERRY DUNCAN

GEORGE BARTON

JAMES BARCLAYAVA WORTH

PAIGE EATON

JORDAN BOCK

10. First, Calgary Transit will probably find it impossible to establish a frame for itstarget population, which is people with disabilities who use Calgary Transit. It willalso have to carefully define what it means by people with disabilities. If this

Copyright 2011 Pearson Canada Inc. 2
http://www.oecd.org/dataoecd/20/26/34350524.pdfhttp://www.oecd.org/dataoecd/20/26/34350524.pdfhttp://www.statcan.ca/english/about/policy/infousers.htmhttp://www.statcan.ca/english/about/policy/infousers.htmhttp://www.dmn.ca/index.htmlhttp://www.dmn.ca/index.htmlhttp://www.statcan.ca/english/about/policy/infousers.htmhttp://www.oecd.org/dataoecd/20/26/34350524.pdf


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means people in wheelchairs, then it will at least be possible to identify such riderswhen an interviewer visits a bus or a bus stop. However, it will be quite difficult forCalgary Transit to obtain a truly random sample of the opinions of people inwheelchairs who use Calgary Transits services. Coverage errors will be practicallyunavoidable. As well, if interviewers are approaching only those riders in

wheelchairs, the survey respondents may be unhappy about being singled outbecause of their wheelchairs. They may refuse to answer the interviewers questions,leading to nonresponse errors. Interviewers will have to be trained carefully toovercome any resulting resistance of survey subjects. Because data will probably becollected on buses or at bus stops, with interviewers recording information while abus is in motion, or possibly during bad weather at a bus stop, processing errors mayoccur. Finally, Calgary Transit will have to be sure that suitably qualified people aredoing the analysis, to avoid estimation errors.


11. This is impossible. A price cannot decrease by more than 100% (and a 100%

decrease would mean the price was 0). It is likely that the company means that theold price is 125% of the current price. So, for example, if the old price was $250,then the new price would be $200. You can see that 250/200 = 1.25 or 125%.

12. The graph with the y-axis that begins at 7,000 is misleading, because it makes theindex decline at the end of 2008 look more dramatic than it actually was. While thefall in the stock market index was significant, using a y-axis that begins with zeroputs it in better perspective.

13. Jane Woodsmans average grade has increased from 13.8% last semester to 16.6%this semester. The provocative language of the initial statement (astonishingprogress, substantial 20%) is inappropriate. As well, the 20% figure, used as it ishere, suggests something different from the facts. Janes grades did increase by20%, but this is only 20% of the original grade of 13.8%, so it is not much of animprovement.

14. Aside from the fact that you should be suspicious of anyone who will not share theactual data with you, the local managers assurance that all is well may not be borneout by fact. Notice that the decrease claimed is in maximumwait times, not averagewait times. It is entirely possible that average waiting times have increased. Youneed to see the data!

15. Yes. There is no distortion in how the data are represented, and the graph is clearlylabelled and easy to understand.


16. No! With such an observational study, this kind of conclusion about cause and effectis not justified. There could be many factors (other than income) that explain whychildren in wealthier families are better off. For example, parents in wealthier



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families may have more confidence, and this may provide a very positiveenvironment in which children flourish.

17. No. Even if the study was randomized (no information is provided), it would not belegitimate to make this conclusion. While taller men are more likely to be married,

we cannot conclude that they are more likely to be married because they are taller.There could be many other factors at work.

18. It may be that the diary system contributed to increased sales. Because the datacompares the same people before and after use of the diary system, there is somesupport for this conclusion. However, notice that only poor performers were selectedfor the trial. These people may have worked harder simply because it was clear theirpoor performance had been noticed.

19. If you had compared the sales performance of a randomly-selected group ofsalespeople (not only poor performers), you would be able to come to a stronger

conclusion about the diary systems impact on increased sales.

20. There may be a cause-and-effect relationship here, but any conclusions should bemade cautiously. For example, hotter weather or a nearby fair for children couldhave increased foot traffic (and sales) during the period.


21.a. In this case, the national manager of quality control probably has a good grasp ofstatistical approaches. While you should still strive for clarity and simplicity, youcan include more of the technical work in the body of the report. Printouts ofcomputer-based analysis would be included in the appendix.

b. While human resources professionals probably have some understanding ofstatistical analysis, they are less likely to understand the details. In this case, youshould write your report with a minimum of statistical jargon. The body of yourreport should contain key results, but the details of your analysis should be saved forthe appendix.

c. In this case, you can assume no statistical expertise in your readers. While youshould still report on how your analysis was conducted, and how you arrived at yourconclusions, you probably would not send this part of the report to your customers.The report you send your boss should be easily understandable to everyone. Thechallenge here will be to make your conclusions easy to understand, while notoversimplifying, or suggesting that your results are stronger than they actually are.

22. It is incorrect to suggest that study of a random sample proves anything. Thisstatement is much more definitive than can be justified. As well, the study was doneon past customers, and may not apply to future customers. Nevertheless, such astudy could be persuasive about what segment of the market the company shouldfocus on.



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23. The average amount of paint in a random sample of 30 cans was 3.012 litres,compared with the target level of 3 litres. This sample mean is within control chartlimits, indicating no need to adjust the paint filling line.

24. Analysis of output for a random sample of 50 workers showed an increase in worker

output from 52 units per hour, on average, to 56 units per hour after the training.This evidence is sufficient to suggest that the worker output increased after training.This may mean that the training caused the increase in output, but this can bedetermined only after an examination of the circumstances, to determine if therewere other possible causes of the increase in output.

25. In fact, some studies have shown that there is a positive relationship between heightand income (that is, taller people tend to have higher incomes). However, all suchstudies must be observational (there is no ethical way to control height!), and so thecause-and-effect conclusion suggested here is not valid. The statement could berewritten as follows: A study has shown a strong positive relationship between

height and income. You might even go on to discourage the unsophisticated readerfrom jumping to conclusions, as follows: Of course, this should not be interpretedas meaning that greater height guarantees higher income, or that you cannot earn ahigh income if you are short.

Chapter Review Exercises

1. Collecting data usually leads to a better understanding of the question and a betterdecision.

2. Businesses may not have all of the data available, because it is impossible or toocostly to collect. For example, it is unlikely that a business would have detailedinformation available about every customer. However, reliable decisions can bemade on the basis of detailed information about a random sample of customers.

3. It is generally not valid to draw conclusions about a population on the basis of aconvenience sample. Because there is no way to estimate the probability of anyparticular element of the population being selected for a convenience sample, wecannot control or estimate the probability of error.

4. Students often use their average grade to summarize their performance in a semester.

5. Decision-makers may not be statisticians. Statistical analysis is powerful only if it iscommunicated so that those making the decision can understand the story the dataare telling.

6. One of the difficulties with gathering data through personal interviews is that thosebeing surveyed are sometimes charmed by the interviewer. This sometimes results ininterviewees acting to please the interviewer, rather than providing honest orinformed responses to questions. Respondents can also be misled by the interviewer,as Rick Mercer so successfully illustrates in the Talking to Americans segments.



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For example, Rick Mercer managed to persuade Americans to congratulateCanadians on legalizing VCRs.

7. It is possible to make reliable conclusions on the basis of 1,003 responses. Thesample size may seem small, when you consider there are millions of adult

Canadians who have retirement funds. However, the sample size required dependsnot on the size of the population, but on its variability. If all Canadians were exactlythe same, a sample of one would be sufficient. The more variable Canadians are, thelarger the sample size required for estimates of a desired level of accuracy. This issomething you will explore more in Chapter 8.

8. No. The applications are filled out by employers, not employees. Employers have avested interest in portraying themselves as top employers. The sample is notrepresentative. The Top 100 are selected from a self-selected sample.

9. Done correctly, such a study could identify a positive relationship between height

and income. However, it is not correct to suggest the study means that height is thecause of the differences in incomes, although if the study was well-designed, othercauses could have been randomized. Still, the leap to evolution as the explanation isnot at all justified by the study. While this may be the explanation, it is only one ofmany possible explanations.

10. You collected your sample results at only one physical location at the school. Sinceit was near the smoking area, it is likely that your sample contained adisproportionate number of smokers. It is likely that smokers opinions about thenew smoking policy would differ from nonsmokers opinions. Your sample isalmost certainly not representative of the entire school community.

11. There are many examples of loyalty programs: Airmiles, Presidents ChoiceFinancial rewards, American Express rewards, HBC rewards, PetroCanadas Petro-Points, Sears Club points, Aeroplan. Enter loyalty rewards programs into anInternet search engine, and you will find references to many such programs.

12. This is an observational study. It is not possible to draw a strong conclusion thatdrinking alcohol causes higher earnings. In fact, the causation may run the other way:higher income may cause more drinking (because those with higher incomes canafford to drink alcohol). The study measured income, not social networks, so theexplanation provided is speculative. As well, there are other factors that couldexplain the differences in incomes, and these were not controlled in the study.

13. The article describes the New Coke story as "the greatest marketing disaster of alltime". The research failed to uncover the attachment people felt to the original Coke.A question such as "Would you switch to the New Coke?" might have revealed howloyal customers were to the original Coke.



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14. The Conference Board included the detail so that anyone reading the study coulddraw their own conclusions about the reliability of the data, and possible biases in thestudy results.

15. While the title used in the report is accurate, the percentage decrease is relatively

small, and the actual number of drivers has increased. The title could easily bemisunderstood.

16. The author has used Excel to generate Lotto 6/49 quick picks, but she didn't win thelottery either!

17. Of course, because your samples are randomly-selected, your samples cannot bepredicted. When the author did this exercise, the sample averages were as shown inthe table below. The population average is 65.0. The sample averages ranged from60.7 to 73.7. Some were quite close to the population average, and the largestdifference between a sample average and the true value was 8.7.

Average Mark from 10 Randomly-Selected Samples of Size 10

60.7 61.8 65.5 65.6 67.4

69.8 70.3 71.3 73.0 73.7

18. Again, the values you obtain cannot be predicted. These averages should be closer tothe true population average, because they are based on more data (15 data pointsinstead of 10). The author's results are shown in the table below. In general, thesample averages are closer to the true population average. The largest difference

between a sample average and the true value is -6.4.

Average Mark from 10 Randomly-Selected Samples of Size 15

58.6 61.2 62.6 64.0 66.2

66.9 67.2 67.7 68.4 70.8

19. Based on the author's results for exercises 17 and 18 above (yours will be different):the average of the sample averages, when the sample size is 10, is 67.9. The averageof the sample averages, when the sample size is 15, is 65.4. The average of the

sample averages is closer to the true population average value when the sample sizeis larger. You will investigate this more in Chapter 6.



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20. a. Because students are generally quite mobile, often moving from the place wherethey attended to school to their place of work after graduating, it may be quitedifficult to contact them for the graduation employment and satisfaction measures.Some graduates will almost certainly be missed, and if their opinions differ fromthose surveyed, the results will not be truly representative.

The same kinds of problem arise with surveys of current students. Such students aresurveyed in their classes, so those who are absent on the day of the survey aremissed. It could be that the opinions of those who are absent are different from theopinions of those who are present in class (for example, it could be the case thatstudents are absent because they do not find their classes relevant to their futurecareers).

Employers may also be missed, so the potential for coverage errors existsthroughout. Of course, as with any survey, all the other nonsampling errors arepossibilities: nonresponse errors, response errors, processing and estimation errors.

This is a large undertaking, and so there are more possibilities for error.

b. Although it could be the case that all colleges improved their services significantlybetween 1999-2000 and later years, this seems unlikely. There may be anotherexplanation for the shift in the percentage of students satisfied with college services.In fact, a closer inspection reveals that about a half-dozen colleges improved theirratings quite significantly. Without more information, there is no way to know whythis happened.

c. The report uses summary measures (percentages of responses for each category, foreach year) and graphs (line graphs and bar graphs) to summarize the data.

d. In 1999-2000, an additional capstone question was included in the calculation. Sincethis question was not used in subsequent years, the average student satisfaction ratesare not directly comparable.

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