Solutions to End-of-Section and Chapter Review Problems 31
CHAPTER 1
1.1 The type of beverage sold yields categorical or “qualitative” respons.
The type of beverage sold yields distinct categories in which no ordering is implied.
1.2 Three sizes of U.S. business are classified into distinct categories—small, medium, and large—
in which order is implied.
1.3 The time it takes to download a video from the Internet is a continuous numerical or
“quantitative” variable becau time can have any value from 0 to any reasonable unit of time.
1.4 (a) The number of cellphones is a numerical variable that is discrete becau the outcome is
a count.
(b) Monthly data usage is a numerical variable that is continuous becau any value within a
range of values can occur.
(c) Number of text messages exchanged per month is a numerical variable that is discrete
becau the outcome is a count.
(d) Voice usage per month is a numerical variable that is continuous becau any value
within a range of values can occur.
(e) Whether a cellphone is ud for email is a categorical variable becau the answer can be
only yes or no.
1.5 (a) numerical, continuous广东省会计
(b) numerical, discrete
(c) categorical
(d) categorical
山西考试招生1.6 (a) Categorical
(b) Numerical, continuous
(c) Categorical
(d) Numerical, discrete
(e) Categorical
1.7 (a) numerical, continuous *
(b) categorical
(c) categorical
(d) numerical, discrete
*Some rearchers consider money as a discrete numerical variable becau it can be “counted.”
1.8 (a) numerical, continuous *
(b) numerical, discrete
(c) numerical, continuous *
(d) categorical
*Some rearchers consider money as a discrete numerical variable becau it can be “counted.”
32 Chapter 1: Defining and Collecting Data
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 becau the respons reprent 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 occupation, marital status, type of clothing.
Numerical questions might be age, average monthly hours shopping for clothing, income.
1.12 The answer depends on the chon data t.
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 u primary data collected through an
obrvational study of the driving characteristics of drivers over the cour of a month.
1.16 The information prented there is bad 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 quences and continue unfinished
quences 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 quences above 902 and duplicates are discarded.
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 quences above 93 and all repeating quences are discarded.
(b) Row 29: 12 47 83 76 22 99 65 93 10 65 83 61 36 98 89 58 86
Note: All quences above 93 are discarded. Elements 65 and 83 are repeated.
Solutions to End-of-Section and Chapter Review Problems 33 1.20 A simple random sample would be less practical for personal interviews becau of travel costs
(unless interviewees are paid to attend a central interviewing location).
1.21 This is a probability sample becau the lection is bad on chance. It is not a simple random
sample becau A is more likely to be lected than B or C.
1.22 Here all members of the population are equally likely to be lected and the sample lection
mechanism is bad on chance. But not every sample of size 2 has the same chance of
being lected. 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 satisfaction 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 with the quality of life may differ by gender
and by experience/class level, a stratified sample using eight strata, female freshmen
through female niors and male freshmen through male niors, could be lected. 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 lect. The population frame is the
registrar’s file of 4,000 student names.晚安北京
(c) A systematic sample is easier to lect by hand from the registrar’s records than a
simple random sample, since an initial person at random is lected and then every 20th
person thereafter would be sampled. The systematic 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 u of a stratified sampling design will not only ensure all
香英文
strata are reprented in the sample, it will also generate a more reprentative 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
我要减肥lected residence hall could be sampled. Since each dormitory has 400 students, a
systematic sample of 200 students can then be lected from the chon cluster of 400
students. Alternately, a cluster could be defined as a floor of one of the 10 dormitories.
Suppo 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 reprentative sample.
34 Chapter 1: Defining and Collecting Data
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 quences above 5000 are discarded. There were no repeating quences.
(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 lected in the simple
random sample are not the same as tho lected in the systematic sample. It would be
highly unlikely that a random process would lect the same units as a systematic
process.
1.25 (a) A stratified sample should be taken so that each of the three strata will be proportionately
reprented.
(b) The number of obrvations in each of the three strata out of the total of 1,000 should
reflect the proportion of the three categories in the customer databa. For example,
3,500/10,000 = 35% so 35% of 1,000 = 350 customers should be lected from the
prospective buyers; similarly 4,500/10,000 = 45% so 450 customers should be lected
from the first time buyers, and 2,000/10,000 = 20% so 200 customers from the repeat
buyers.
(c) It is not simple random sampling becau, unlike the simple random sampling, it ensures
proportionate reprentation across the entire population.
第一个工会组织
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 lected? What sampling design was ud? What mode of respon was ud: a personal
interview, a telephone interview, or a mail survey? Were interviewers trained? Were survey
questions field-tested? What questions were asked? Were they clear, accurate, unbiad, valid?
What operational definition of “vast majority” was ud? What was the respon rate? What was the sample size?
1.27 (a) Possible coverage error: Only employees in a specific division of the company were
sampled.
(b) Possible nonrespon 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.
情谊深厚的成语
(d) Possible measurement error: Ambiguous wording in questions asked on the
questionnaire.
Solutions to End-of-Section and Chapter Review Problems 35 1.28 The results are bad on an online survey. If the frame is suppod to be small business owners,
how is the population defined? This is a lf-lecting sample of people who responded online, so there is an undefined nonrespon error. Sampling error cannot be determined since this is not a random sample.
1.29 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 lected? What was the frame being ud? What sampling design was ud?
What mode of respon was ud: a personal interview, a telephone interview, or a mail survey?
Were interviewers trained? Were survey questions field-tested? What other questions were
asked? Were they clear, accurate, unbiad, and valid? What was the respon rate? What was the margin of error? What was the sample size?
1.30 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 lected?
What sampling design was ud? What mode of respon was ud: a personal interview, a
telephone interview, or a mail survey? Were interviewers trained? Were survey questions field-买碟
tested? What other questions were asked? Were the questions clear, accurate, unbiad, and
valid? What was the respon rate? What was the margin of error? What was the sample size?
What frame was ud?
1.31 A population contains all the items of interest whereas a sample contains only a portion of the
items in the population.
1.32 A statistic is a summary measure describing a sample whereas a parameter is a summary measure
describing an entire population.
1.33 Categorical random variables yield categorical respons such as yes or no answers. Numerical
random variables yield numerical respons such as your height in inches.
1.34 Discrete random variables produce numerical respons that ari from a counting process.
Continuous random variables produce numerical respons that ari from a measuring process.
1.35 Items or individuals in a probability sampling are lected bad on known probabilities while
items or individuals in a nonprobability samplings are lected without knowing their
probabilities of lection.
1.36 Microsoft Excel could be ud to perform various statistical computations that were possible only
with a slide-rule or hand-held calculator in the old days.
1.37 (a) The population of interest was 18-54 year olds who currently own a smartphone and/or
tablet, and who u and do not u the devices to shop.
(b) The sample was the 1,003 18-54 year olds who currently own a smartphone and/or tablet,
who u and do not u the devices to shop, and who responded to the study.
(c) A parameter of interest is the proportion of all tablet urs in the population who u their
device to purcha product and rvices.
(d) A statistic ud to estimate the parameter of interest in (c) is the proportion of tablet urs
in the sample who u their device to purcha product and rvices.
