Type:
Solution Manual
Resource:
Basic Business Statistics Concepts and Applications
Edition:
5th Edition
Author(s):
Mark Berenson David Levine Kathryn Szabat Martin O’Brien Nicole Jayne Judith Watson
Chapter 1: Defining and collecting data Learning objectives After studying this chapter you should be able to: 1. identify how statistics is used in business 2. recognise the sources of data used in business 3. identify the types of data used in business
4. 5.
distinguish between different survey sampling methods evaluate the quality of surveys
1.1
(a) (b)
1.2
Three sizes of coffee cups are classified into distinct categories — small, medium and large — in which order is implied.
1.3
(a) (b)
The type of beverage sold yields categorical or ‘qualitative’ responses. The type of beverage sold yields distinct categories in which no ordering is implied.
The time it takes to download a video from the Internet yields numerical or ‘quantitative’ responses. The download time is a ratio scaled variable because the true zero point in the measurement is zero units of time.
1.4
(a) (b) (c) (d)
Numerical, discrete, ratio scale Numerical, continuous, ratio scale Categorical, nominal scale Categorical, nominal scale
1.5
(a) (b) (c) (d)
Numerical, continuous, ratio scale Numerical, discrete, ratio scale Categorical, nominal scale Categorical, nominal scale
1.6
(a) (b) (c) (d)
Categorical, nominal scale Numerical, continuous, ratio scale Numerical, discrete, ratio scale Numerical, discrete, ratio scale
1.7
(a) Numerical, continuous, ratio scale* (b) Numerical, discrete, ratio scale (c) Numerical, continuous, ratio scale* (d) Categorical, nominal *Some researchers consider money as a discrete numerical variable because it can be ‘counted’.
Copyright © 2019 Pearson Australia (a division of Pearson Australia Group Pty Ltd) 9781488617249, Berenson, Basic Business Statistics 5e
1.8
(a) (b) (c)
1.9
(a) (b)
Income may be considered discrete if we ‘count’ our money. It may be considered continuous if we ‘measure’ our money; we are only limited by the way a country’s monetary system treats its currency. The first format is preferred because the responses represent data measured on a higher scale. The first format would bring a greater response because it has a large number of possible income levels, as opposed to a limited number of income groups in the second format. The population is ‘all Australian working women’. A systematic or random sample could be taken of Australian working women. The director might wish to collect both numerical and categorical data. Three categorical questions might be occupation, marital status and type of clothing purchased online. Numerical questions might be age, average monthly hours shopping online for clothing and income.
1.10
An experiment will be carried out in artificial conditions and will try to assess people’s attitudes to making charitable donations. These may differ in real-life situations. A survey of the same subjects will rely on self-reporting. Respondents may not always report accurately if they are trying to appear more generous.
1.11
The company is likely to have more data relating to its own sales. It can use invoices to retailers, if it is a wholesaler, or records of cash and credit card purchases, if it is a retailer. For competitors, it will have access to advertised prices from the media or online advertisements but may not know the sales volumes.
1.12
The answers to this question depend on which datafile is selected.
1.13
The answers to this question depend on which poll or news story is selected.
1.14
The answers to this question depend on which story is selected.
1.15
The data source will depend on what driving characteristics are being studied and the type of vehicle. It could be tachographs as used in heavy vehicles, dash cameras, GPS monitors and other equipment. However, surveys of drivers or log books might also be used.
1.16
The answer to this question will depend on the panel chosen.
1.17
(a) (b) (c)
1.18
Sample without replacement: read from left to right in 3-digit sequences and continue unfinished sequences from end of row to beginning of next row. Row 05: 338; 505; 855; 551; 438; 855; 077; 186; 579; 488; 767; 833; 170 Row 05-06: 897 Row 06: 340; 033; 648; 847; 204; 334; 639; 193; 639; 411; 095; 924 Row 06-07: 707 Row 07: 054; 329; 776; 100; 871; 007; 255; 980; 646; 886; 823; 920; 461 Row 08: 893; 829; 380; 900; 796; 959; 453; 410; 181; 277; 660; 908; 887 Row 08-09: 237 Row 09: 818; 721; 426; 714; 050; 785; 223; 801; 670; 353; 362; 449 Row 09-10: 406
001 040 902
Copyright © 2019 Pearson Australia (a division of Pearson Australia Group Pty Ltd) 9781488617249, Berenson, Basic Business Statistics 5e
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Note: all sequences above 902 are discarded. 1.19
(a) (b)
Row 29: 12; 47; 83; 76; 22; 99; 65; 93; 10; 65; 83; 61; 36; 98; 89; 58; 86; 92; 71 Note: all sequences above 93 and all repeating sequences are discarded. Row 29: 12; 47; 83; 76; 22; 99; 65; 93; 10; 65; 83; 61; 36; 98; 89; 58; 86 Note: all sequences above 93 are discarded. Elements 65 and 83 are repeated.
1.20
A simple random sample would be less practical for personal interviews because of travel costs (unless interviewees are paid to attend a central interviewing location).
1.21
This is a probability sample because the selection is based on chance. It is not a simple random sample because A is more likely to be selected than B or C.
1.22
Here all members of the population are equally likely to be selected and the sample selection mechanism is based on chance. But not every sample of size 2 has the same chance of being selected. For example, the sample “’B and C’ is impossible.
1.23
(a)
(b) (c)
(d)
(e)
1.24
(a) (b)
As a complete list of voters exists, a simple random sample of 2,000 voters could be taken. If attitudes to urban consolidation randomly fluctuate across the alphabetical listing of voters, a systematic 1-in-20 sample could also be taken from the population frame. If attitudes may differ by gender and by ward of residence, a stratified sample using eight strata could be selected. If attitudes to urban consolidation are thought to fluctuate as much within clusters as between them, a cluster sample could be taken. A simple random sample is one of the simplest to select. The population frame is the council’s list of 40,000 voters’ names. A systematic sample is easier to select by hand from the council’s records than a simple random sample, since an initial person at random is selected and then every 20th person thereafter would be sampled. The systematic sample would have the additional benefit that the alphabetical distribution of sampled voters’ names would be more comparable to the alphabetic distribution of voters’ names in the population. However, if certain ethnic groups were more likely to be concentrated alphabetically and they have particular attitudes to urban consolidation due to their cultural background, then this method may introduce bias. If lists by gender and ward of residence are readily available, a stratified sample should be taken. Since attitudes to urban consolidation may indeed differ by gender and area of residence, the use of a stratified sampling design will ensure all strata are represented in the sample. It will also generate a more representative sample and produce estimates of the population parameter that have greater precision. People who already live in high-rise apartments are likely to have different views about urban consolidation from those living in low-density areas. Systematic sampling by street is likely to lead to selection bias if a high proportion of streets in one ward is chosen. A stratified sample should be taken so that each of the four strata will be proportionately represented. Since the stratum may differ in the invoice amount, it may be more important to sample a larger percentage of invoices in stratum 1 and stratum 2, and smaller percentages in stratum 3 and stratum 4. For example, 50/5000 = 1% so 1% of 500 = 5 invoices should be selected from stratum 1; similarly 10% = 50 should be selected from stratum 2, 20% = 100 from stratum 3, and 69% = 345 from stratum 4.
Copyright © 2019 Pearson Australia (a division of Pearson Australia Group Pty Ltd) 9781488617249, Berenson, Basic Business Statistics 5e
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(c)
It is not simple random sampling because, unlike the simple random sampling, it ensures proportionate representation across the entire population.
1.25
Before accepting the results of a survey of university students, you might want to know, for example: Who funded the survey? Why was it conducted? What was the population from which the sample was selected? What sampling design was used? What mode of response was used: a personal interview, a telephone interview or a mail survey? Were interviewers trained? Were survey questions fieldtested? What questions were asked? Were they clear, accurate, unbiased, and valid? What operational definition of ‘vast majority’ was used? What was the response rate? What was the sample size?
1.26
(a) (b) (c) (d)
Possible coverage error: only employees in a specific division of the company were sampled. Possible non-response error: no attempt is made to contact non-respondents to urge them to complete the evaluation of job satisfaction. Possible sampling error: the sample statistics obtained from the sample will not be equal to the parameters of interest in the population. Possible measurement error: ambiguous wording in questions in the questionnaire.
1.27
Before accepting the results of the survey, you might want to know, for example: Who funded the study? Why was it conducted? What was the population from which the sample was selected? What sampling design was used? What mode of response was used: a computer based survey, a personal interview, a telephone interview or a mail survey? Were interviewers trained? Were survey questions field-tested? How were cybercrime and millennials defined? What other questions were asked? Were they clear, accurate, unbiased and valid? What was the response rate? What was the margin of error? What was the sample size? What was the frame being used?
1.28
Before accepting the results of the survey, the environmental economist might want to know, for example: Who funded the study? Was it a special interest group? Why was it conducted? What was the population from which the sample was selected? What was the sample size? What was the frame being used? What sampling design was used? What mode of response was used: in a less developed country telephones will not be commonly found in village homes, so was this a personal interview or a mail survey? In what languages were the questions written? What is the literacy rate in Kiribati? Were interviewers trained? Were survey questions field-tested? What other questions were asked? Were they clear, accurate, unbiased and valid? What was the response rate?
Copyright © 2019 Pearson Australia (a division of Pearson Australia Group Pty Ltd) 9781488617249, Berenson, Basic Business Statistics 5e
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