Solutions to End-of-Section and Chapter Review Problems 41
Copyright ©2015 Pearson Education, Inc. CHAPTER 1
1.1 (a) The type of beverage sold yi elds categorical or “qualitative” responses.
(b) The type of beverage sold yields dis tinct categories in which no ordering is implied.
1.2 Three sizes of U.S. businesses are classified into distinct categories—small, medium, and large—
in which order is implied.
1.3 (a) The time it takes to download a video from the Internet is a continuous numerical or
“quantitative” variable because time can have any value from 0 to any reasonable unit of
time.
(b) The download time is a ratio scaled va riable because the true zero point in the
measurement is zero units of time.
1.4 (a) The number of cellphones is a numerical variable that is discrete because the outcome is
a count. It is ratio scaled because it has a true zero point.
(b) Monthly data usage is a numerical variab le that is continuous because any value within a
range of values can occur. It is ratio scaled because it has a true zero point.
(c) Number of text messages exchanged per month is a numerical variable that is discrete
because the outcome is a count. It is ratio scaled because it has a true zero point.
(d) Voice usage per month is a numerical va riable that is continuous because any value
within a range of values can occur. It is ratio scaled because it has a true zero point.
(e) Whether a cellphone is used for email is a categorical variable because the answer can be
only yes or no. This also makes it a nominal-scaled variable.
1.5 (a) numerical, continuous, ratio scale (b) numerical, discrete, ratio scale (c) categorical, nominal scale (d) categorical, nominal scale 1.6 (a) Categorical, nominal scale. (b) Numerical, continuous, ratio scale. (c) Categorical, nominal scale. (d) Numerical, discrete, ratio scale. (e) Categorical, nominal scale. 1.7 (a) numerical, continuous, ratio scale * (b) categorical, nominal scale (c) categorical, nominal scale (d) numerical, discrete, ratio scale
*Some researchers consider money as a discrete numerical variable because it can be “counted.”
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42 Chapter 1: Defining and Collecting Data
Copyright ©2015 Pearson Education, Inc. 1.8 (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.”
1.9 (a) 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.
(b) The first format is preferred because the responses represent data measured on a higher
scale.
1.10 The underlying variable, ability of the students, may be continuous, but the measuring device, the
test, does not have enough precision to distinguish between the two students.
1.11 (a) The population is “all working women from the metropolitan area.” A systematic or random
sample could be taken of women from the metropolitan area. The director might wish to collect both numerical and categorical data.
(b) Three categorical questions might be o ccupation, marital status, type of clothing.
Numerical questions might be age, average monthly hours shopping for clothing, income. 1.12 The answer depends on the chosen data set. 1.13 The answer depends on the specific story. 1.14 The answer depends on the specific story. 1.15 The transportation engineers and planners should use primary data collected through an
observational study of the driving characteristics of drivers over the course of a month.
1.16 The information presented there is based mainly on a mixture of data distributed by an
organization and data collected by ongoing business activities.
1.17 (a) 001 (b) 040 (c) 902 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 Rows 05-06: 897 Row 06: 340 033 648 847 204 334 639 193 639 411 095 924 Rows 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 Rows 08-09: 237 Row 09: 818 721 426 714 050 785 223 801 670 353 362 449 Rows 09-10: 406 Note: All sequences above 902 and duplicates are discarded.
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Solutions to End-of-Section and Chapter Review Problems 43
Copyright ©2015 Pearson Education, Inc. 1.19 (a) 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 a ll repeating sequences are discarded.
(b) 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 ever y sample of size 2 has the same chance of
being selected. For example the sample “B and C” is impossible.
1.23 (a) Since a complete roster of full-time students exists, a simple random sample of 200
students could be taken. If student satisfac tion with the quality of campus life randomly
fluctuates across the student body, a systematic 1-in-20 sample could also be taken from the population frame. If student satisfaction w ith the quality of life may differ by gender
and by experience/class level, a stratified sample using eight strata, female freshmen
through female seniors and male freshmen through male seniors, could be selected. If
student satisfaction with the quality of life is thought to fluctuate as much within clusters
as between them, a cluster sample could be taken.
(b) A simple random sample is one of the simplest to select. The population frame is the
registrar’s file of 4,000 student names.
(c) A systematic sample is easier to select by hand from the registrar’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 syst ematic sample would have the additional
benefit that the alphabetic distribution of sampled students’ names would be more
comparable to the alphabetic distribution of student names in the campus population.
(d) If rosters by gender and class designations are readily available, a stratified sample should be taken. Since student satisfaction with the quality of life may indeed differ by
gender and class level, the use of a stratified sampling design will not only 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.
(e) If all 4,000 full-time students reside in one of 10 on-campus residence halls which fully
integrate students by gender and by class, a cluster sample should be taken. A cluster
could be defined as an entire residence hall, and the students of a single randomly selected residence hall could be sampled. Since each dormitory has 400 students, a systematic sample of 200 students can then be selected from the chosen cluster of 400 students. Alternately, a cluster could be de fined as a floor of one of the 10 dormitories.
Suppose there are four floors in each dormitory with 100 students on each floor. Two floors could be randomly sampled to produce the required 200 student sample. Selection of an entire dormitory may make distribution and collection of the survey easier to accomplish. In contrast, if there is some variable other than gender or class that differs across dormitories, sampling by floor may produce a more representative sample.
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44 Chapter 1: Defining and Collecting Data
Copyright ©2015 Pearson Education, Inc. 1.24 (a) Row 16: 2323 6737 5131 8888 1718 0654 6832 4647 6510 4877
Row 17: 4579 4269 2615 1308 2455 7830 5550 5852 5514 7182 Row 18: 0989 3205 0514 2256 8514 4642 7567 8896 2977 8822 Row 19: 5438 2745 9891 4991 4523 6847 9276 8646 1628 3554 Row 20: 9475 0899 2337 0892 0048 8033 6945 9826 9403 6858 Row 21: 7029 7341 3553 1403 3340 4205 0823 4144 1048 2949 Row 22: 8515 7479 5432 9792 6575 5760 0408 8112 2507 3742 Row 23: 1110 0023 4012 8607 4697 9664 4894 3928 7072 5815 Row 24: 3687 1507 7530 5925 7143 1738 1688 5625 8533 5041 Row 25: 2391 3483 5763 3081 6090 5169 0546 Note: All sequences above 5000 are discarde d. There were no repeating sequences.
(b) 089 189 289 389 489 589 689 789 889 989 1089 1189 1289 1389 1489 1589 1689 1789 1889 1989 2089 2189 2289 2389 2489 2589 2689 2789 2889 2989 3089 3189 3289 3389 3489 3589 3689 3789 3889 3989 4089 4189 4289 4389 4489 4589 4689 4789 4889 4989 (c) With the single exception of invoice #0989, the invoices selected in the simple random sample are not the same as those selected in the systematic sample. It would be
highly unlikely that a random process would select the same units as a systematic process.
1.25 (a) A stratified sample should be taken so that each of the four strata will be proportionately
represented.
(b) 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.
(c) It is not simple random sampling because, unlike the simple random sampling, it ensures
proportionate representation across the entire population.
1.26 Before accepting the results of a survey of college 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? Wh at mode of response was used: a personal
interview, a telephone interview, or a mail surv ey? Were interviewers trained? Were survey
questions field-tested? What questions were asked? Were they clear, accurate, unbiased, valid?
What operational definition of “vast majority” w as used? What was the response rate? What was
the sample size?
1.27 (a) Possible coverage error: Only employ ees in a specific division of the company were
sampled.
(b) Possible nonresponse error: No attempt is made to contact nonrespondents to urge them
to complete the evaluation of job satisfaction.
(c) Possible sampling error: The sample statistics obtained from the sample will not be equal
to the parameters of interest in the population.
(d) Possible measurement error: Ambiguous wording in questions asked on the
questionnaire.
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