Solutions for Chapter 1
Section 1.1
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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.
d
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
yg
no gaps between the bars of a histogram.
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
en
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.
1.7 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
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of days.
s2
47
??
??
Note, there are no gaps between the bars.
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.
? ?
Copyright ©2024 Pearson Education, Inc.
1
, 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.
tu
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.
d
1.15
yg
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
en
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
iu
asking them to return the completed survey by mail.
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
s2
data for those people who required medical attention.
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
47
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.
??
1.21. 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.
1.23 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.
? ?
Copyright ©2024 Pearson Education, Inc.
2
, Section 1.3
1.25.
a. Because the population is spread over a large geographical area, a cluster random sample could
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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.
d
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,
yg
that is to say a sample, is a statistic.
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
en
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.
1.31 Values computed from a sample are always considered statistics. In order for a value, such as an
iu
average, to be considered a parameter it must be computed from all items in the population.
1.33 Using Excel, choose the Data tab, select Data Analysis from the Analysis Group , then Random
Number Generation – shown as follows:
s2
47
??
??
??
? ?
Copyright ©2024 Pearson Education, Inc.
3
, The next step is to complete the random number generation dialog as follows:
tu
d yg
en
The resulting random numbers generated are:
iu
s2
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.
47
1.35 This is a statistic. A poll would be a sample of eligible voters rather than all eligible voters.
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.
??
1.39 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.
1.41
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.
?
Copyright ©2024 Pearson Education, Inc.
4
Section 1.1
tu
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.
d
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
yg
no gaps between the bars of a histogram.
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
en
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.
1.7 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
iu
of days.
s2
47
??
??
Note, there are no gaps between the bars.
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.
? ?
Copyright ©2024 Pearson Education, Inc.
1
, 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.
tu
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.
d
1.15
yg
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
en
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
iu
asking them to return the completed survey by mail.
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
s2
data for those people who required medical attention.
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
47
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.
??
1.21. 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.
1.23 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.
? ?
Copyright ©2024 Pearson Education, Inc.
2
, Section 1.3
1.25.
a. Because the population is spread over a large geographical area, a cluster random sample could
tu
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.
d
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,
yg
that is to say a sample, is a statistic.
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
en
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.
1.31 Values computed from a sample are always considered statistics. In order for a value, such as an
iu
average, to be considered a parameter it must be computed from all items in the population.
1.33 Using Excel, choose the Data tab, select Data Analysis from the Analysis Group , then Random
Number Generation – shown as follows:
s2
47
??
??
??
? ?
Copyright ©2024 Pearson Education, Inc.
3
, The next step is to complete the random number generation dialog as follows:
tu
d yg
en
The resulting random numbers generated are:
iu
s2
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.
47
1.35 This is a statistic. A poll would be a sample of eligible voters rather than all eligible voters.
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.
??
1.39 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.
1.41
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.
?
Copyright ©2024 Pearson Education, Inc.
4
