Solution Manual for Business Statistics, Global Edition, 10th Edition
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SOLUTIONS MANUAL
B USINESS S TATISTICS
A D ECISION -M AKING A PPROACH
T ENTH EDITION
David F. Groebner
Boise State University
Patrick W. Shannon
Boise State University
Phillip C. Fry
Boise State University
B USINESS S TATISTICS
A D ECISION -M AKING A PPROACH
T ENTH EDITION
David F. Groebner
Boise State University
Patrick W. Shannon
Boise State University
Phillip C. Fry
Boise State University
iii
Contents
Chapter 1 The Where, Why, and How of Data Collection 1
Section 1.1 1
Section 1.2 3
Section 1.3 5
Section 1.4 8
End of Chapter Exercises 8
Chapter 2 Graphs, Charts, and Tables—Describing Your Data 11
Section 2.1 11
Section 2.2 28
Section 2.3 43
End of Chapter Exercises 53
Chapter 3 Describing Data Using Numerical Measures 63
Section 3.1 63
Section 3.2 76
Section 3.3 86
End of Chapter Exercises 94
Chapter 4 Introduction to Probability 113
Section 4.1 113
Section 4.2 121
End of Chapter Exercises 134
Chapter 4 Questions 139
Chapter 5 Discrete Probability Distributions 145
Section 5.1 145
Section 5.2 155
Section 5.3 166
End of Chapter Exercises 173
Chapter 6 Introduction to Continuous Probability Distributions 181
Section 6.1 181
Business Application 187
Section 6.2 196
End of Chapter Exercises 201
Chapter 7 Introduction to Sampling Distributions 209
Section 7.1 209
Section 7.2 218
Section 7.3 228
End of Chapter Exercises 240
Chapter 8 Estimating Single Population Parameters 249
Section 8.1 249
Section 8.2 262
Section 8.3 271
End of Chapter Exercises 280
Contents
Chapter 1 The Where, Why, and How of Data Collection 1
Section 1.1 1
Section 1.2 3
Section 1.3 5
Section 1.4 8
End of Chapter Exercises 8
Chapter 2 Graphs, Charts, and Tables—Describing Your Data 11
Section 2.1 11
Section 2.2 28
Section 2.3 43
End of Chapter Exercises 53
Chapter 3 Describing Data Using Numerical Measures 63
Section 3.1 63
Section 3.2 76
Section 3.3 86
End of Chapter Exercises 94
Chapter 4 Introduction to Probability 113
Section 4.1 113
Section 4.2 121
End of Chapter Exercises 134
Chapter 4 Questions 139
Chapter 5 Discrete Probability Distributions 145
Section 5.1 145
Section 5.2 155
Section 5.3 166
End of Chapter Exercises 173
Chapter 6 Introduction to Continuous Probability Distributions 181
Section 6.1 181
Business Application 187
Section 6.2 196
End of Chapter Exercises 201
Chapter 7 Introduction to Sampling Distributions 209
Section 7.1 209
Section 7.2 218
Section 7.3 228
End of Chapter Exercises 240
Chapter 8 Estimating Single Population Parameters 249
Section 8.1 249
Section 8.2 262
Section 8.3 271
End of Chapter Exercises 280
iii
Contents
Chapter 1 The Where, Why, and How of Data Collection 1
Section 1.1 1
Section 1.2 3
Section 1.3 5
Section 1.4 8
End of Chapter Exercises 8
Chapter 2 Graphs, Charts, and Tables—Describing Your Data 11
Section 2.1 11
Section 2.2 28
Section 2.3 43
End of Chapter Exercises 53
Chapter 3 Describing Data Using Numerical Measures 63
Section 3.1 63
Section 3.2 76
Section 3.3 86
End of Chapter Exercises 94
Chapter 4 Introduction to Probability 113
Section 4.1 113
Section 4.2 121
End of Chapter Exercises 134
Chapter 4 Questions 139
Chapter 5 Discrete Probability Distributions 145
Section 5.1 145
Section 5.2 155
Section 5.3 166
End of Chapter Exercises 173
Chapter 6 Introduction to Continuous Probability Distributions 181
Section 6.1 181
Business Application 187
Section 6.2 196
End of Chapter Exercises 201
Chapter 7 Introduction to Sampling Distributions 209
Section 7.1 209
Section 7.2 218
Section 7.3 228
End of Chapter Exercises 240
Chapter 8 Estimating Single Population Parameters 249
Section 8.1 249
Section 8.2 262
Section 8.3 271
End of Chapter Exercises 280
Contents
Chapter 1 The Where, Why, and How of Data Collection 1
Section 1.1 1
Section 1.2 3
Section 1.3 5
Section 1.4 8
End of Chapter Exercises 8
Chapter 2 Graphs, Charts, and Tables—Describing Your Data 11
Section 2.1 11
Section 2.2 28
Section 2.3 43
End of Chapter Exercises 53
Chapter 3 Describing Data Using Numerical Measures 63
Section 3.1 63
Section 3.2 76
Section 3.3 86
End of Chapter Exercises 94
Chapter 4 Introduction to Probability 113
Section 4.1 113
Section 4.2 121
End of Chapter Exercises 134
Chapter 4 Questions 139
Chapter 5 Discrete Probability Distributions 145
Section 5.1 145
Section 5.2 155
Section 5.3 166
End of Chapter Exercises 173
Chapter 6 Introduction to Continuous Probability Distributions 181
Section 6.1 181
Business Application 187
Section 6.2 196
End of Chapter Exercises 201
Chapter 7 Introduction to Sampling Distributions 209
Section 7.1 209
Section 7.2 218
Section 7.3 228
End of Chapter Exercises 240
Chapter 8 Estimating Single Population Parameters 249
Section 8.1 249
Section 8.2 262
Section 8.3 271
End of Chapter Exercises 280
iv
Chapter 9 Introduction to Hypothesis Testing 285
Section 9.1 285
Computer Database Exercises 289
Section 9.2 291
Section 9.3 299
End of Chapter Exercises 309
Chapter 10 Estimation and Hypothesis Testing for Two Population Parameters 319
Section 10.1 319
Section 10.2 326
Section 10.3 335
Section 10.4 344
End of Chapter Exercises 350
Chapter 11 Hypothesis Tests and Estimation for Population Variances 357
Section 11.1 357
Section 11.2 365
End of Chapter Exercises 368
Chapter 12 Analysis of Variance 373
Section 12.1 373
Section 12.2 385
Section 12.3 396
End of Chapter Exercises 406
Chapter 13 Goodness-of-Fit Tests and Contingency Analysis 417
Section 13.1 417
Section 13.2 425
End of Chapter Exercises 437
Business Applications 438
Chapter 14 Introduction to Linear Regression and Correlation Analysis 445
Section 14.1 445
Section 14.2 455
Section 14.3 471
End of Chapter Exercises 481
Chapter 15 Multiple Regression Analysis and Model Building 491
Section 15.1 491
Section 15.2 499
Section 15.3 506
Section 15.4 521
Section 15.5 530
End of Chapter Exercises 548
Chapter 16 Analyzing and Forecasting Time-Series Data 569
Section 16.1 569
Section 16.2 572
Database Exercises 590
Section 16.3 595
Business Applications 599
End of Chapter Exercises 607
Chapter 9 Introduction to Hypothesis Testing 285
Section 9.1 285
Computer Database Exercises 289
Section 9.2 291
Section 9.3 299
End of Chapter Exercises 309
Chapter 10 Estimation and Hypothesis Testing for Two Population Parameters 319
Section 10.1 319
Section 10.2 326
Section 10.3 335
Section 10.4 344
End of Chapter Exercises 350
Chapter 11 Hypothesis Tests and Estimation for Population Variances 357
Section 11.1 357
Section 11.2 365
End of Chapter Exercises 368
Chapter 12 Analysis of Variance 373
Section 12.1 373
Section 12.2 385
Section 12.3 396
End of Chapter Exercises 406
Chapter 13 Goodness-of-Fit Tests and Contingency Analysis 417
Section 13.1 417
Section 13.2 425
End of Chapter Exercises 437
Business Applications 438
Chapter 14 Introduction to Linear Regression and Correlation Analysis 445
Section 14.1 445
Section 14.2 455
Section 14.3 471
End of Chapter Exercises 481
Chapter 15 Multiple Regression Analysis and Model Building 491
Section 15.1 491
Section 15.2 499
Section 15.3 506
Section 15.4 521
Section 15.5 530
End of Chapter Exercises 548
Chapter 16 Analyzing and Forecasting Time-Series Data 569
Section 16.1 569
Section 16.2 572
Database Exercises 590
Section 16.3 595
Business Applications 599
End of Chapter Exercises 607
v
Chapter 17 Introduction to Nonparametric Statistics 629
Section 17.1 629
Section 17.2 634
Section 17.3 645
End of Chapter Exercises 650
Chapter 18 Introducing Business Analytics 659
Section 18.1 659
Chapter 19 Introduction to Decision Analysis (Online) 669
Section 19.1 669
Business Applications 671
Section 19.2
Skill Development 677
Business Applications 678
Section 19.3
Business Applications 680
End of Chapter Exercises
Business Applications 684
Chapter 20 Introduction to Quality and Statistical Process Control (Online) 695
Section 20.1 695
End of Chapter Exercises 710
Chapter 17 Introduction to Nonparametric Statistics 629
Section 17.1 629
Section 17.2 634
Section 17.3 645
End of Chapter Exercises 650
Chapter 18 Introducing Business Analytics 659
Section 18.1 659
Chapter 19 Introduction to Decision Analysis (Online) 669
Section 19.1 669
Business Applications 671
Section 19.2
Skill Development 677
Business Applications 678
Section 19.3
Business Applications 680
End of Chapter Exercises
Business Applications 684
Chapter 20 Introduction to Quality and Statistical Process Control (Online) 695
Section 20.1 695
End of Chapter Exercises 710
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1
Chapter 1: The Where, Why, and How of Data Collection
Section 1.1
1.1. This application is primarily descriptive in nature. The owner wishes to develop a presentation.
She will most likely use charts, graphs, tables and numerical measures to describe her data.
1.2. The graph is a bar chart. A bar chart displays values associated with categories. In this case the
categories are the departments at the food store. The values are the total monthly sales (in
dollars) in each department. A bar chart also typically has gaps between the bars. A histogram
has no gaps and the horizontal axis represents the possible values for a numerical variable.
1.3. A bar chart is used whenever you want to display data that has already been categorized while a
histogram is used to display data over a range of values for the factor under consideration.
Another fundamental difference is that there typically are gaps between the bars on a bar chart but
there are no gaps between the bars of a histogram.
1.4. Businesses often make claims about their products that can be tested using hypothesis testing.
For example, it is not enough for a pharmaceutical company to claim that its new drug is effective
in treating a disease. In order for the drug to be approved by the Food and Drug Administration
the company must present sufficient evidence that the drug first does no harm and that it also
provides an effective treatment against the disease. The claims that the drug does no harm and is
an effective treatment can be tested using hypothesis testing.
1.5. The company could use statistical inference to determine if its parts last longer. Because it is not
possible to examine every part that could be produced the company could examine a randomly
chosen subset of its parts and compare the average life of the subset to the average life of a
randomly chosen subset of the competitor’s parts. By using statistical inference procedures the
company could reach a conclusion about whether its parts last longer or not.
1.6. Student answers will vary depending on the periodical selected and the periodical's issue date, but
should all address the three parts of the question.
Chapter 1: The Where, Why, and How of Data Collection
Section 1.1
1.1. This application is primarily descriptive in nature. The owner wishes to develop a presentation.
She will most likely use charts, graphs, tables and numerical measures to describe her data.
1.2. The graph is a bar chart. A bar chart displays values associated with categories. In this case the
categories are the departments at the food store. The values are the total monthly sales (in
dollars) in each department. A bar chart also typically has gaps between the bars. A histogram
has no gaps and the horizontal axis represents the possible values for a numerical variable.
1.3. A bar chart is used whenever you want to display data that has already been categorized while a
histogram is used to display data over a range of values for the factor under consideration.
Another fundamental difference is that there typically are gaps between the bars on a bar chart but
there are no gaps between the bars of a histogram.
1.4. Businesses often make claims about their products that can be tested using hypothesis testing.
For example, it is not enough for a pharmaceutical company to claim that its new drug is effective
in treating a disease. In order for the drug to be approved by the Food and Drug Administration
the company must present sufficient evidence that the drug first does no harm and that it also
provides an effective treatment against the disease. The claims that the drug does no harm and is
an effective treatment can be tested using hypothesis testing.
1.5. The company could use statistical inference to determine if its parts last longer. Because it is not
possible to examine every part that could be produced the company could examine a randomly
chosen subset of its parts and compare the average life of the subset to the average life of a
randomly chosen subset of the competitor’s parts. By using statistical inference procedures the
company could reach a conclusion about whether its parts last longer or not.
1.6. Student answers will vary depending on the periodical selected and the periodical's issue date, but
should all address the three parts of the question.
Loading page 7...
2 Business Statistics: A Decision-Making Approach, Tenth Edition
1.7. The appropriate chart in this case is a histogram where the horizontal axis contains the number of
missed days and the height of the bars represent the number of employees who missed each
number of days
Histogram: Missed Days for Illness or Injury
0
20
40
60
80
100
120
140
160
180
0-2 days 3-5 days 6-8 days 8-10 days
Days Missed
Number of Employees
Note, there are no gaps between the bars.
1.8. Because it would be too costly, too time consuming, or practically impossible to contact every
subscriber to ascertain the desired information, the decision makers at Fortune might decide to
use statistical inference, particularly estimation, to answer its questions. By looking at a subset of
the data and using the procedures of estimation it would be possible for the decision makers to
arrive at values for average age and average income that are within tolerable limits of the actual
values.
1.9. Student answers will vary depending on the business periodical or newspaper selected and the
article referenced. Some representative examples might include estimates of the number of
CEO's who will vote for a particular candidate, estimates of the percentage increase in wages for
factory workers, estimates of the average dollar advertising expenditures for pharmaceutical
companies in a specific year, and the expected increase in R&D expenditures for the coming
quarter.
1.10. Student answers will vary. However, the examples should illustrate how statistics has been used
and should clearly indicate the type of statistical analysis employed.
1.7. The appropriate chart in this case is a histogram where the horizontal axis contains the number of
missed days and the height of the bars represent the number of employees who missed each
number of days
Histogram: Missed Days for Illness or Injury
0
20
40
60
80
100
120
140
160
180
0-2 days 3-5 days 6-8 days 8-10 days
Days Missed
Number of Employees
Note, there are no gaps between the bars.
1.8. Because it would be too costly, too time consuming, or practically impossible to contact every
subscriber to ascertain the desired information, the decision makers at Fortune might decide to
use statistical inference, particularly estimation, to answer its questions. By looking at a subset of
the data and using the procedures of estimation it would be possible for the decision makers to
arrive at values for average age and average income that are within tolerable limits of the actual
values.
1.9. Student answers will vary depending on the business periodical or newspaper selected and the
article referenced. Some representative examples might include estimates of the number of
CEO's who will vote for a particular candidate, estimates of the percentage increase in wages for
factory workers, estimates of the average dollar advertising expenditures for pharmaceutical
companies in a specific year, and the expected increase in R&D expenditures for the coming
quarter.
1.10. Student answers will vary. However, the examples should illustrate how statistics has been used
and should clearly indicate the type of statistical analysis employed.
Loading page 8...
Chapter 1: The Where, Why, and How of Data Collection 3
Section 1.2
1.11. As discussed in this section, the pet store would most likely use a written survey or a telephone
survey to collect the customer satisfaction data.
1.12. A leading question is one that is designed to elicit a specific response, or one that might influence
the respondent’s answer by its wording. The question is posed so that the respondent believes the
researcher has a specific answer in mind when the question is asked, or worded in such a way that
the respondent feels obliged to provide an answer consistent with the question. For example, a
question such as “Do you agree with the experts who recommend that more tax dollars be given
to clean up dangerous and unhealthy pollution?” could cause respondents to provide the answer
that they think will be consistent with the “experts” with whom they do not want to disagree.
Leading question should be avoided in surveys because they may introduce bias.
1.13. An experiment is any process that generates data as its outcome. The plan for performing the
experiment in which the variable of interest is defined is referred to as an experimental design. In
the experimental design one or more factors are identified to be changed so that the impact on the
variable of interest can be observed or measured.
1.14. There will likely by a high rate of nonresponse bias since many people who work days will not be
home during the 9–11 AM time slot. Also, the data collectors need to be careful where they get
the phone number list as some people do not have listed phones in phone books and others have
no phone or only a cell phone. This may result in selection bias.
1.15. a. Observation would be the most likely method. Observers could be located at various bike
routes and observe the number of riders with and without helmets. This would likely be
better than asking people if they wear a helmet since the popular response might be to say yes
even when they don’t always do so.
b. A telephone survey to gas stations in the state. This could be a cost effective way of getting
data from across the state. The respondent would have the information and be able to provide
the correct price.
c. A written survey of passengers. This could be given out on the plane before the plane lands
and passengers could drop the surveys in a box as they de-plane. This method would likely
garner higher response rates compared to sending the survey to passengers’ mailing address
and asking them to return the completed survey by mail.
1.16. The two types of validity mentioned in the section are internal validity and external validity. For
this problem external validity is easiest to address. It simply means the sampling method chosen
will be sufficient to insure the results based on the sample will be able to be generalized to the
population of all students. Internal validity would involve making sure the data gathering
method, for instance a questionnaire, accurately determines the respondent’s attitude toward the
registration process.
1.17. This data could have been collected through a survey. Employees of the USDA could provide
periodic reports of fire ant activity in their region. Also, medical reports could be used to collect
data assuming people with bites had required medical attention.
1.18. There are many potential sources of bias associated with data collection. If data is to be collected
using personal interviews it will be important that the interviewer be trained so that interviewer
bias, arising from the way survey questions are asked, is not injected into the survey. If the
survey is conducted using either a mail survey or a telephone survey then it is important to be
aware of nonresponse bias from those who do not respond to the mailing or refuse to answer your
Section 1.2
1.11. As discussed in this section, the pet store would most likely use a written survey or a telephone
survey to collect the customer satisfaction data.
1.12. A leading question is one that is designed to elicit a specific response, or one that might influence
the respondent’s answer by its wording. The question is posed so that the respondent believes the
researcher has a specific answer in mind when the question is asked, or worded in such a way that
the respondent feels obliged to provide an answer consistent with the question. For example, a
question such as “Do you agree with the experts who recommend that more tax dollars be given
to clean up dangerous and unhealthy pollution?” could cause respondents to provide the answer
that they think will be consistent with the “experts” with whom they do not want to disagree.
Leading question should be avoided in surveys because they may introduce bias.
1.13. An experiment is any process that generates data as its outcome. The plan for performing the
experiment in which the variable of interest is defined is referred to as an experimental design. In
the experimental design one or more factors are identified to be changed so that the impact on the
variable of interest can be observed or measured.
1.14. There will likely by a high rate of nonresponse bias since many people who work days will not be
home during the 9–11 AM time slot. Also, the data collectors need to be careful where they get
the phone number list as some people do not have listed phones in phone books and others have
no phone or only a cell phone. This may result in selection bias.
1.15. a. Observation would be the most likely method. Observers could be located at various bike
routes and observe the number of riders with and without helmets. This would likely be
better than asking people if they wear a helmet since the popular response might be to say yes
even when they don’t always do so.
b. A telephone survey to gas stations in the state. This could be a cost effective way of getting
data from across the state. The respondent would have the information and be able to provide
the correct price.
c. A written survey of passengers. This could be given out on the plane before the plane lands
and passengers could drop the surveys in a box as they de-plane. This method would likely
garner higher response rates compared to sending the survey to passengers’ mailing address
and asking them to return the completed survey by mail.
1.16. The two types of validity mentioned in the section are internal validity and external validity. For
this problem external validity is easiest to address. It simply means the sampling method chosen
will be sufficient to insure the results based on the sample will be able to be generalized to the
population of all students. Internal validity would involve making sure the data gathering
method, for instance a questionnaire, accurately determines the respondent’s attitude toward the
registration process.
1.17. This data could have been collected through a survey. Employees of the USDA could provide
periodic reports of fire ant activity in their region. Also, medical reports could be used to collect
data assuming people with bites had required medical attention.
1.18. There are many potential sources of bias associated with data collection. If data is to be collected
using personal interviews it will be important that the interviewer be trained so that interviewer
bias, arising from the way survey questions are asked, is not injected into the survey. If the
survey is conducted using either a mail survey or a telephone survey then it is important to be
aware of nonresponse bias from those who do not respond to the mailing or refuse to answer your
Loading page 9...
4 Business Statistics: A Decision-Making Approach, Tenth Edition
calls. You must also be careful when selecting your survey subjects so that selection bias is not a
problem. In order to have useful, reliable data that is representative of the true student opinions
regarding campus food service, it is necessary that the data collection process be conducted in a
manner that reduces or eliminates the potential for these and other sources of potential bias.
1.19. For retailers technology that scans the product UPC code at checkout makes the collection of data
fast and accurate. Retailers that use such technology can automatically update their inventory
records and develop an extensive collection of customer buying habits. By applying advanced
statistical techniques to the data the retailer can identify relationships among purchases that might
otherwise go unnoticed. Such information could enable retailers to target their advertising or
even rearrange the placement of products in the store to increase sales. Manufacturing firms use
bar code scanning to collect information concerning product availability and product quality.
Credit card purchases are automatically tracked by the retailer and the bankcard company. In this
way the credit card company is able to track your purchases and even alert you to potential fraud
if purchases on your card appear to be unusual. Finally, some companies are using radio
frequency identification (RFID) to track products through their supply chain, so that product
delays and inventory problems can be minimized.
1.20. One advantage of this form of data gathering is the same as for mail questionnaires. That is low
cost. Additional factors being speed of delivery and, with current software, with closed- ended
questions, instant updating of data analysis. Disadvantages are also similar, in particular low
response and potential confusion about questions. An additional factor might be the ability of
competitors to “hack” into the database and analysis program.
1.21. Student answers will vary. Look for clarity of questions and to see that the issue questions are
designed to gather useful data. Look for appropriate demographic questions.
1.22. Students should select some form of personal observation as the data-gathering technique. In
addition, there should be a discussion of a sampling procedure with an effort made to ensure the
sample randomly selected both days of the week unless daily observations are made, and
randomly selected times of the day since 24 hour observation would likely be impossible. A
complete answer would also address efforts to reduce the potential bias of having an observer
standing in an obvious manner by the displays.
1.23. Student answers will vary. However, the issue questions should be designed to gather the desired
data regarding customers’ preferences for the use of the space. Demographic questions should
provide data so that the responses can be broken down appropriately so that United Fitness Center
managers can determine which subset of customers have what opinion about this issue.
Regarding questionnaire layout, look at neatness and answer location space. Make sure questions
are properly worded, used reasonable vocabulary, and are not leading questions.
1.24. The results of the survey are based on telephone interviews with 744 adults, aged 18 and older.
Students may also answer that the survey could have been conducted using a written survey via
mail questionnaire or internet survey. Because telephone interviews were used to collect the
survey data nonresponse biases associated with sampled adults who are not at home when
phoned, or adults who refuse to participate in the survey. There is also the problem that some
adults do not have a landline phone. If written surveys are used to collect the data then it is
important to guard against nonresponse bias from those sampled adults who do not complete the
survey There is also the problem of selection bias. In phone interviews we may miss the people
who work evenings and nights. If written surveys are used we must be careful to select a
representative sample of the adult population.
calls. You must also be careful when selecting your survey subjects so that selection bias is not a
problem. In order to have useful, reliable data that is representative of the true student opinions
regarding campus food service, it is necessary that the data collection process be conducted in a
manner that reduces or eliminates the potential for these and other sources of potential bias.
1.19. For retailers technology that scans the product UPC code at checkout makes the collection of data
fast and accurate. Retailers that use such technology can automatically update their inventory
records and develop an extensive collection of customer buying habits. By applying advanced
statistical techniques to the data the retailer can identify relationships among purchases that might
otherwise go unnoticed. Such information could enable retailers to target their advertising or
even rearrange the placement of products in the store to increase sales. Manufacturing firms use
bar code scanning to collect information concerning product availability and product quality.
Credit card purchases are automatically tracked by the retailer and the bankcard company. In this
way the credit card company is able to track your purchases and even alert you to potential fraud
if purchases on your card appear to be unusual. Finally, some companies are using radio
frequency identification (RFID) to track products through their supply chain, so that product
delays and inventory problems can be minimized.
1.20. One advantage of this form of data gathering is the same as for mail questionnaires. That is low
cost. Additional factors being speed of delivery and, with current software, with closed- ended
questions, instant updating of data analysis. Disadvantages are also similar, in particular low
response and potential confusion about questions. An additional factor might be the ability of
competitors to “hack” into the database and analysis program.
1.21. Student answers will vary. Look for clarity of questions and to see that the issue questions are
designed to gather useful data. Look for appropriate demographic questions.
1.22. Students should select some form of personal observation as the data-gathering technique. In
addition, there should be a discussion of a sampling procedure with an effort made to ensure the
sample randomly selected both days of the week unless daily observations are made, and
randomly selected times of the day since 24 hour observation would likely be impossible. A
complete answer would also address efforts to reduce the potential bias of having an observer
standing in an obvious manner by the displays.
1.23. Student answers will vary. However, the issue questions should be designed to gather the desired
data regarding customers’ preferences for the use of the space. Demographic questions should
provide data so that the responses can be broken down appropriately so that United Fitness Center
managers can determine which subset of customers have what opinion about this issue.
Regarding questionnaire layout, look at neatness and answer location space. Make sure questions
are properly worded, used reasonable vocabulary, and are not leading questions.
1.24. The results of the survey are based on telephone interviews with 744 adults, aged 18 and older.
Students may also answer that the survey could have been conducted using a written survey via
mail questionnaire or internet survey. Because telephone interviews were used to collect the
survey data nonresponse biases associated with sampled adults who are not at home when
phoned, or adults who refuse to participate in the survey. There is also the problem that some
adults do not have a landline phone. If written surveys are used to collect the data then it is
important to guard against nonresponse bias from those sampled adults who do not complete the
survey There is also the problem of selection bias. In phone interviews we may miss the people
who work evenings and nights. If written surveys are used we must be careful to select a
representative sample of the adult population.
Loading page 10...
Chapter 1: The Where, Why, and How of Data Collection 5
Section 1.3
1.25. a. Because the population is spread over a large geographical area, a cluster random sample
could be selected to reduce travel costs.
b. A stratified random sample would probably be used to keep sample size as small as possible.
c. Most likely a convenience sample would be used since doing a statistical sample would be
too difficult.
1.26. To determine the range of employee numbers for the first employee selected in a systematic
random sample use the following:
Population Size 18,000
Part Range 180
Sample Size 100
Thus, the first person selected will come from employees 1–180. Once that person is randomly
selected, the second person will be the one numbered 180 higher than the first, and so on.
1.27. Whenever a descriptive numerical measure such as an average is calculated from the entire
population it is a parameter. The corresponding measure calculated from a subset of the
population, that is to say a sample, is a statistic.
1.28. Statistical sampling techniques consist of those sampling methods that select samples based on
chance. Nonstatistical sampling techniques consist of those methods of selecting samples using
convenience, judgment, or other nonchance processes. In convenience sampling, samples are
chosen because they are easy or convenient to sample. There is no attempt to randomize the
selection of the selected items. In convenience sampling not every item in the population has a
random chance of being selected. Rather, items are sampled based on their convenience alone.
Thus, convenience sampling is not a statistical sampling method.
1.29. From a numbered list of all customers who own a certificate of deposit the bank would need to
randomly determine a starting point between 1 and k, where k would be equal to
25000/1000 = 25. This could be done using a random number table or by having a statistical
package or a spreadsheet generate a random number between 1 and 25. Once this value is
determined the bank would select that numbered customer as the first sampled customer and then
select every 25th customer after that until 100 customers are sampled.
1.30. A census is an enumeration of the entire set of measurements taken from the population as a
whole. While in some cases, the items of interest are obtained from people such as through a
survey, in many instances the items of interest come from a product or other inanimate object.
For example, a study could be conducted to determine the defect rate for items made on a
production line. The census would consist of all items produced on the line in a defined period of
time.
1.31. Values computed from a sample are always considered statistics. In order for a value, such as an
average, to be considered a parameter it must be computed from all items in the population.
1.32. In stratified random sampling, the population is divided into homogeneous groups called strata.
The idea is to make all items in a stratum as much alike as possible with respect to the variable of
interest thereby reducing the number of items that will need to be sampled from each stratum. In
cluster sampling, the idea is to break the population into heterogeneous groups called clusters
(usually on a geographical basis) such that each cluster looks as much like the original population
Section 1.3
1.25. a. Because the population is spread over a large geographical area, a cluster random sample
could be selected to reduce travel costs.
b. A stratified random sample would probably be used to keep sample size as small as possible.
c. Most likely a convenience sample would be used since doing a statistical sample would be
too difficult.
1.26. To determine the range of employee numbers for the first employee selected in a systematic
random sample use the following:
Population Size 18,000
Part Range 180
Sample Size 100
Thus, the first person selected will come from employees 1–180. Once that person is randomly
selected, the second person will be the one numbered 180 higher than the first, and so on.
1.27. Whenever a descriptive numerical measure such as an average is calculated from the entire
population it is a parameter. The corresponding measure calculated from a subset of the
population, that is to say a sample, is a statistic.
1.28. Statistical sampling techniques consist of those sampling methods that select samples based on
chance. Nonstatistical sampling techniques consist of those methods of selecting samples using
convenience, judgment, or other nonchance processes. In convenience sampling, samples are
chosen because they are easy or convenient to sample. There is no attempt to randomize the
selection of the selected items. In convenience sampling not every item in the population has a
random chance of being selected. Rather, items are sampled based on their convenience alone.
Thus, convenience sampling is not a statistical sampling method.
1.29. From a numbered list of all customers who own a certificate of deposit the bank would need to
randomly determine a starting point between 1 and k, where k would be equal to
25000/1000 = 25. This could be done using a random number table or by having a statistical
package or a spreadsheet generate a random number between 1 and 25. Once this value is
determined the bank would select that numbered customer as the first sampled customer and then
select every 25th customer after that until 100 customers are sampled.
1.30. A census is an enumeration of the entire set of measurements taken from the population as a
whole. While in some cases, the items of interest are obtained from people such as through a
survey, in many instances the items of interest come from a product or other inanimate object.
For example, a study could be conducted to determine the defect rate for items made on a
production line. The census would consist of all items produced on the line in a defined period of
time.
1.31. Values computed from a sample are always considered statistics. In order for a value, such as an
average, to be considered a parameter it must be computed from all items in the population.
1.32. In stratified random sampling, the population is divided into homogeneous groups called strata.
The idea is to make all items in a stratum as much alike as possible with respect to the variable of
interest thereby reducing the number of items that will need to be sampled from each stratum. In
cluster sampling, the idea is to break the population into heterogeneous groups called clusters
(usually on a geographical basis) such that each cluster looks as much like the original population
Loading page 11...
6 Business Statistics: A Decision-Making Approach, Tenth Edition
as possible. Then clusters are randomly selected and from the cluster, individual items are
selected using a statistical sampling method.
1.33. Using Excel, choose the Data tab, select Data Analysis from the Analysis Group , then Random
Number Generation—shown as follows:
The next step is to complete the random number generation dialog as follows:
The resulting random numbers generated are:
as possible. Then clusters are randomly selected and from the cluster, individual items are
selected using a statistical sampling method.
1.33. Using Excel, choose the Data tab, select Data Analysis from the Analysis Group , then Random
Number Generation—shown as follows:
The next step is to complete the random number generation dialog as follows:
The resulting random numbers generated are:
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Chapter 1: The Where, Why, and How of Data Collection 7
Note, the students’ answers may differ since Excel generates different streams of random
numbers each time it is used. Also, if the application requires integer numbers, the Decrease
Decimal option can be used.
1.34. If these percentages were based on all students attending college in those years they would be
parameters, if the percentages were based on a sample they would be statistics.
1.35. This is a statistic. A poll would be a sample of eligible voters rather than all eligible voters.
1.36. Solution
a. Stratified random sampling
b. Simple random sampling or possibly cluster random sampling
c. Systematic random sampling
d. Stratified random sampling
1.37. This is a statistical sample. Every employee has an equal chance of being selected using this
method. In fact, this is an example of a simple random sample because every possible sample of
size 50 has an equal chance of being selected.
1.38. a. Student answers will vary
b. Cluster sampling could be used to ensure that you get all types of cereal. Make each cluster
the area where certain cereals are located (i.e., isle, row, shelf, etc.)
c. Cluster sampling would give you a better idea of the inventory of all types of cereal. Simple
random sampling could possibly end up with only looking at 2 or 3 cereal types.
1.39. Students should choose the Data tab, select Data Analysis from the Analysis group—Random
Number Generation process. Students’ answers will differ since Excel generates different
streams of random numbers each time it is used, but 40 random numbers should be generated
from a uniform distribution with values ranging from 1 to 578. Since the application requires
integer numbers, the Decrease Decimal option should be used.
1.40. a. The population should be all users of cross-country ski lots and trailheads in Colorado.
b. Several sampling techniques could be selected. Be sure that some method of ensuring
randomness is discussed. In addition, some students might give greater weight to frequent
users of the lots. In which case the population would really be user days rather than
individual users.
c. Students using Excel should choose the Data tab, select Data Analysis from the Analysis
group—Random Number Generation process. Students’ answers may differ since Excel
generates different streams of random numbers each time it is used. Since the application
requires integer numbers, the Decrease Decimal option should be used.
1.41. a. Since there are 4,000 patient files we could give each file a unique identification number
consisting of 4 digits. The first file would be given the identification number “0001.” The
last file would be given the identification number of “4000.” By assigning each patient a
number and randomly selecting the 100 numbers allows each possible sample of 100 an equal
chance of being selected.
b. Either use a random number table (randomly select the starting row and column), or use a
computer program, such as Microsoft Excel, which has a random number generator.
c. Since each patient is assigned a 4-digit identification number, we would need a 4-digit
random number for each random number selected.
d. Answers will vary.
Note, the students’ answers may differ since Excel generates different streams of random
numbers each time it is used. Also, if the application requires integer numbers, the Decrease
Decimal option can be used.
1.34. If these percentages were based on all students attending college in those years they would be
parameters, if the percentages were based on a sample they would be statistics.
1.35. This is a statistic. A poll would be a sample of eligible voters rather than all eligible voters.
1.36. Solution
a. Stratified random sampling
b. Simple random sampling or possibly cluster random sampling
c. Systematic random sampling
d. Stratified random sampling
1.37. This is a statistical sample. Every employee has an equal chance of being selected using this
method. In fact, this is an example of a simple random sample because every possible sample of
size 50 has an equal chance of being selected.
1.38. a. Student answers will vary
b. Cluster sampling could be used to ensure that you get all types of cereal. Make each cluster
the area where certain cereals are located (i.e., isle, row, shelf, etc.)
c. Cluster sampling would give you a better idea of the inventory of all types of cereal. Simple
random sampling could possibly end up with only looking at 2 or 3 cereal types.
1.39. Students should choose the Data tab, select Data Analysis from the Analysis group—Random
Number Generation process. Students’ answers will differ since Excel generates different
streams of random numbers each time it is used, but 40 random numbers should be generated
from a uniform distribution with values ranging from 1 to 578. Since the application requires
integer numbers, the Decrease Decimal option should be used.
1.40. a. The population should be all users of cross-country ski lots and trailheads in Colorado.
b. Several sampling techniques could be selected. Be sure that some method of ensuring
randomness is discussed. In addition, some students might give greater weight to frequent
users of the lots. In which case the population would really be user days rather than
individual users.
c. Students using Excel should choose the Data tab, select Data Analysis from the Analysis
group—Random Number Generation process. Students’ answers may differ since Excel
generates different streams of random numbers each time it is used. Since the application
requires integer numbers, the Decrease Decimal option should be used.
1.41. a. Since there are 4,000 patient files we could give each file a unique identification number
consisting of 4 digits. The first file would be given the identification number “0001.” The
last file would be given the identification number of “4000.” By assigning each patient a
number and randomly selecting the 100 numbers allows each possible sample of 100 an equal
chance of being selected.
b. Either use a random number table (randomly select the starting row and column), or use a
computer program, such as Microsoft Excel, which has a random number generator.
c. Since each patient is assigned a 4-digit identification number, we would need a 4-digit
random number for each random number selected.
d. Answers will vary.
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8 Business Statistics: A Decision-Making Approach, Tenth Edition
Section 1.4
1.42. a. Time-series
b. Cross-sectional
c. Time-series
d. Cross-sectional
1.43. Qualitative data are categories or numerical values that represent categories. Quantitative data is
data that is purely numerical.
1.44. a. Ordinal—categories with defined order
b. Nominal—categories with no defined order
c. Ratio
d. Nominal—categories with no defined order
1.45. Nominal data involves placing observations in separate categories according to some measurable
characteristic. Ordinal data also involves placing observations into separate categories, but the
categories can be rank-ordered.
1.46. Since the circles involve a ranking from best to worst, this would be ordinal data.
1.47. a. The data are cross-sectional. The data are collected from 2,300 customers at approximately
the same point in time
b. This is a ratio level, quantitative variable. The data represent a measurement of time.
c. Ordinal with a numerical value representing customers rating of level of service
1.48. a. Nominal Data
b. Ratio Data
c. Ratio Data
d. Ratio Data
e. Nominal
1.49. a. Cross-sectional
b. Time-series
c. Cross-sectional
d. Cross-sectional
e. Time-Series
1.50. Columns A–G are nominal—they are all codes
Columns H–L are ratio level.
End of Chapter Exercises
1.51. Answers will vary with the student. But a good discussion should include the following factors:
Sampling techniques and possible problems selecting a representative sample.
Determining how to develop questions to measure approval.
Structuring questions to avoid bias.
The measurement scale associated with the questions.
The fact these polls tend to develop time-series data.
Section 1.4
1.42. a. Time-series
b. Cross-sectional
c. Time-series
d. Cross-sectional
1.43. Qualitative data are categories or numerical values that represent categories. Quantitative data is
data that is purely numerical.
1.44. a. Ordinal—categories with defined order
b. Nominal—categories with no defined order
c. Ratio
d. Nominal—categories with no defined order
1.45. Nominal data involves placing observations in separate categories according to some measurable
characteristic. Ordinal data also involves placing observations into separate categories, but the
categories can be rank-ordered.
1.46. Since the circles involve a ranking from best to worst, this would be ordinal data.
1.47. a. The data are cross-sectional. The data are collected from 2,300 customers at approximately
the same point in time
b. This is a ratio level, quantitative variable. The data represent a measurement of time.
c. Ordinal with a numerical value representing customers rating of level of service
1.48. a. Nominal Data
b. Ratio Data
c. Ratio Data
d. Ratio Data
e. Nominal
1.49. a. Cross-sectional
b. Time-series
c. Cross-sectional
d. Cross-sectional
e. Time-Series
1.50. Columns A–G are nominal—they are all codes
Columns H–L are ratio level.
End of Chapter Exercises
1.51. Answers will vary with the student. But a good discussion should include the following factors:
Sampling techniques and possible problems selecting a representative sample.
Determining how to develop questions to measure approval.
Structuring questions to avoid bias.
The measurement scale associated with the questions.
The fact these polls tend to develop time-series data.
Loading page 14...
Chapter 1: The Where, Why, and How of Data Collection 9
1.52. Nominal data or ordinal data.
1.53. Interval or ratio data.
1.54. Ratings are typical uses of ordinal scale data. And since ratings are based on personal opinion,
even though people are using the same scale, a direct comparison between the two ratings is not
possible. This is a common problem when people are asked to rate an object using an ordinal
scale.
1.55. Answers will vary with the student. But a good discussion should include the following factors:
Sampling techniques and possible problems selecting a representative sample.
Determining how to measure confidence.
Structuring questions to avoid bias.
The measurement scale associated with the questions.
The fact this poll is specifically intended to develop time-series data.
1.56. Answers will vary with the student.
1.57. Answers will vary with the student.
1.58. a. No because a random sample means that every item in the population has an equal chance of
being selected. Individuals who do not have or use email do not have an equal chance of
being included in this survey. Also, volunteer emails would not be random.
b. In this survey the biggest drawback is that only individuals with strong feelings one way or
the other are apt to respond to this survey. This could lead to a great deal of bias in the
results of the survey. Another big problem with a survey is nonresponse bais. Again because
they are requesting viewers to write in there will be a great deal of nonresponse to this
survey. I would also include in the answer that the question being asked is somewhat leading.
The phrase “using too much force in routine traffic stops” implies that, in fact, force is being
used which one would not expect in a routine traffic stop.
1.59. a. They would probably want to sample the salsa jars as they come off the assembly line at the
plant for a specified time period. They would want to use a random sample. One method
would be to take a systematic random sample. They could then calculate the percentage of
the sample that had an unacceptable thickness.
b. The product is going to be ruined after testing it. You would not want to ruin the entire
product that comes off the assembly line.
1.60. a. Student answers will vary but one method would be personal observation at grocery stores or
another method would be to simply look at their sales. Are buyers of the energy drinks
purchasing bottles or cans?
b. If using personal observation just have people at grocery stores observe people over a
specified period of time and note which are selecting cans and which are selecting bottles and
look at the percentages of each.
c. You would be looking at ratio data because you could have a true 0 if, for example, no one
purchased bottles.
d. Depends on the way the data are collected. Sales data would be quantitative.
1.52. Nominal data or ordinal data.
1.53. Interval or ratio data.
1.54. Ratings are typical uses of ordinal scale data. And since ratings are based on personal opinion,
even though people are using the same scale, a direct comparison between the two ratings is not
possible. This is a common problem when people are asked to rate an object using an ordinal
scale.
1.55. Answers will vary with the student. But a good discussion should include the following factors:
Sampling techniques and possible problems selecting a representative sample.
Determining how to measure confidence.
Structuring questions to avoid bias.
The measurement scale associated with the questions.
The fact this poll is specifically intended to develop time-series data.
1.56. Answers will vary with the student.
1.57. Answers will vary with the student.
1.58. a. No because a random sample means that every item in the population has an equal chance of
being selected. Individuals who do not have or use email do not have an equal chance of
being included in this survey. Also, volunteer emails would not be random.
b. In this survey the biggest drawback is that only individuals with strong feelings one way or
the other are apt to respond to this survey. This could lead to a great deal of bias in the
results of the survey. Another big problem with a survey is nonresponse bais. Again because
they are requesting viewers to write in there will be a great deal of nonresponse to this
survey. I would also include in the answer that the question being asked is somewhat leading.
The phrase “using too much force in routine traffic stops” implies that, in fact, force is being
used which one would not expect in a routine traffic stop.
1.59. a. They would probably want to sample the salsa jars as they come off the assembly line at the
plant for a specified time period. They would want to use a random sample. One method
would be to take a systematic random sample. They could then calculate the percentage of
the sample that had an unacceptable thickness.
b. The product is going to be ruined after testing it. You would not want to ruin the entire
product that comes off the assembly line.
1.60. a. Student answers will vary but one method would be personal observation at grocery stores or
another method would be to simply look at their sales. Are buyers of the energy drinks
purchasing bottles or cans?
b. If using personal observation just have people at grocery stores observe people over a
specified period of time and note which are selecting cans and which are selecting bottles and
look at the percentages of each.
c. You would be looking at ratio data because you could have a true 0 if, for example, no one
purchased bottles.
d. Depends on the way the data are collected. Sales data would be quantitative.
Loading page 15...
10 Business Statistics: A Decision-Making Approach, Tenth Edition
1.61. a. The fact that the friend has selected his favorite players means that all players did not have a
chance of being selected in the sample. The sample would be biased toward the type of
players the friend favors.
b. One method would be to obtain a list of all NBA players. Then assign each player a number.
Then you could use Excel’s random number generator to obtain a random sample of 40
players from the list.
1.62. The appropriate design would be a stratified random sampling method. Start by dividing the
students into class standing (Freshman, Sophomore, Junior, and Senior). Then randomly select
students from each strata.
1.61. a. The fact that the friend has selected his favorite players means that all players did not have a
chance of being selected in the sample. The sample would be biased toward the type of
players the friend favors.
b. One method would be to obtain a list of all NBA players. Then assign each player a number.
Then you could use Excel’s random number generator to obtain a random sample of 40
players from the list.
1.62. The appropriate design would be a stratified random sampling method. Start by dividing the
students into class standing (Freshman, Sophomore, Junior, and Senior). Then randomly select
students from each strata.
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