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N'(t) = dN/dt = 4e^(−0.05t) for (0 ≤ t ≤ 20)
∫dN = ∫ 4e^(− 0.05t) dt
N = 4[1/(- 0.05)] e^(−0.05t) + C
N = - 80 e^(−0.05t) + C
when t = 0, N = 65
65 = - 80 e^[(- 0.05)(0)] + C
C -80 = 65
C = 145
N(t) = 145 - 80 e^(−0.05t) for (0 ≤ t ≤ 20)
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Chapter 16 Case Study
(Foot Locker), pages 618-619. (Start with “Supposing Foot Locker”) Hint: Use
the chi-square test of independence formula on page 610 to compute by hand or
go to: http://www.physics.csbsju.edu/stats/contingency_NROW_NCOLUMN_form.html (Links
to an external site.)Foot Locker in the Shoe MixFoot Locker, Inc., is the world's number one
retailer of athletic footwear and apparel. Headquartered in New York City, the
company has over 44,000 employees and 3369 retail stores in 23 countries across
North America, Europe, Australia, and New Zealand operating under such brand
names as Foot Locker, Lady Foot Locker, Kids Foot Locker, Footaction, Champs
Sports, and CCS. Foot Locker estimates that it controls about 18% of the U.S.
$15 billion athletic footwear market. The company intends to increase its share
of the worldwide market by adding additional stores and by growing its Internet
and catalog business.
In recent years, Foot Locker officials have
been rethinking the company's retail mix. Determining the shoe mix that will maximize
profits is an important decision for Foot Locker. By the year 2002, in an
effort to stock more lower-priced footwear, the company had reduced its
inventory of sneakers priced at $120 or more by 50%.
DISCUSSION
Suppose the data
presented below represented the number of unit sales (million $) for athletic
footwear in the years 2000 and 2012. Use techniques presented in this chapter
to analyze these data and discuss the business implications for Foot Locker.
Price Category
2000
2012
Less than $30
115
126
$30-less than
$40
38
40
$40-less than
$50
37
35
$50-less than
$60
30
27
$60-less than
$70
22
20
$70-less than
$85
21
20
$85-less than
$100
11
11
$100 or more
17
18
Suppose Foot Locker
strongly encourages its employees to make formal suggestions to improve the
store, the product, and the working environment. Suppose a quality auditor
keeps records of the suggestions, the persons who submitted them, and the
geographic region from which they come. A possible breakdown of the number of
suggestions over a 3-year period by employee sex and geographic location
follows. Is there any relationship between the sex of the employee and the
geographic location in terms of number of suggestions? If they are related,
what does this relationship mean to the company? What business implications
might there be for such an analysis?
Sex
Male
Female
U.S. West
29
43
U.S. South
48
20
Location
U.S. East
52
61
U.S. North
28
25
Europe
78
32
Australia
47
29
3.
16.1
The Financial
database contains seven different types of companies. These seven are denoted
by the variable Type. Use a chi-square goodness-of-fit test to determine
whether the seven types of companies are uniformly distributed in this
database.
4.
16.2
In the Manufacturing
database, is the Value of Industrial Shipments (a four-category variable)
uniformly distributed across the database?
5.
16.3
Use a chi-square
test of independence to determine whether Control is independent of Service
in the Hospital database. Comment on the results of this test.
6.
16.4
In the Consumer
database, is Location independent of Region? Use a chi-square test of
independence to answer the question.
2.
Click this link
http://www.physics.csbsju.edu/stats/contingency_NROW_NCOLUMN_form.html
Input '6' for number of rows and '2' for number of columns,
click 'submit', then you will see a new page with blank cells, type the data in
the given problem into those cells, then click 'Calculate now' to see the
results.
Interpret the
results.
For supplemental file, click on the following link: BUS6780_M5HomeworkAssignment
#2.docx
3.
Chapter 12 Case
Study (Caterpillar), pages 471-472, question 1 only. Use an alpha of
.05. You need to submit your supporting formula work or work in
Excel.
The United States Department of Agriculture
(USDA), in conjunction with the Forest Service, publishes information to assist
companies in estimating the cost of building a temporary road for such
activities as a timber sale. Such roads are generally built for one or two
seasons of use for limited traffic and are designed with the goal of
reestablishing vegetative cover on the roadway and adjacent disturbed area
within ten years after the termination of the contract, permit, or lease. The
timber sale contract requires out sloping, removal of culverts and ditches, and
building water bars or cross ditches after the road is no longer needed. As
part of this estimation process, the company needs to estimate haul costs. The
USDA publishes variable costs in dollars per cubic-yard-mile of hauling dirt
according to the speed with which the vehicle can drive. Speeds are mainly
determined by the road width, the sight distance, the grade, the curves and the
turnouts. Thus, on a steep, narrow, winding road, the speed is slow; and on a
flat, straight, wide road, the speed is faster. Shown below are data on speed,
cost per cubic yard for a 12 cubic yard end-dump vehicle, and cost per cubic
yard for a 20 cubic yard bottom-dump vehicle. Use these data and simple
regression analysis to develop models for predicting the haul cost by speed for
each of these two vehicles. Discuss the strength of the models. Based on the
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vehicles.
SPEED (MPH)
HAUL COST
12-CUBIC-YARD END-DUMP VEHICLE $ PER CUBIC YD.
HAUL COST
20-CUBIC-YARD BOTTOM-DUMP VEHICLE $ PER CUBIC YD.
10
$2.46
$1.98
15
$1.64
$1.31
20
$1.24
$0.98
25
$0.98
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30
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40
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Progress CheckUse this activity to assess whether you and your peers can: Based on information about a sampling distribution of sample proportions, use the Normal Distribution Calculator to find a two-tailed probability.Learn by DoingUse the rubric at the bottom of this page as a guide for completing this assignment.DirectionsSubmit your work:Commit a good-faith effort to address all items in the Prompt section below. Please be sure to number your responses.Complete your assigned peer reviews:After you submit your initial good-faith attempt, continue to the ANSWER(S) page and review your instructor's response. But please do not submit your corrected work yet.Within three days after the due date, return to this assignment and complete your assigned peer reviews (directions (Links to an external site.)).Submit your corrected work:We all learn from mistakes (our own and our classmates' mistakes). So please do not immediately correct your own mistakes. If possible, wait until you receive feedback from at least one of your peers. If necessary, correct your work and resubmit the entire assignment. Your instructor will only review and grade your most recent submission, so please do not refer to a previous submission.PromptRecall the use of data from the National Health Survey to estimate behaviors such as alcohol consumption, cigarette smoking, and hours of sleep for all U.S. adults. In the 2005-2007 report, they estimated that 30% of all current smokers started smoking before the age of 16.Suppose that we randomly select 100 U.S. adults who are smokers and find that 25% of this sample started smoking before the age of 16. Is this much error surprising? Find the probability that a sample proportion will be an over- or underestimate of the parameter by more than 5%.I
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Chapter 16 Case Study
(Foot Locker), pages 618-619. (Start with “Supposing Foot Locker”) Hint: Use
the chi-square test of independence formula on page 610 to compute by hand or
go to: http://www.physics.csbsju.edu/stats/contingency_NROW_NCOLUMN_form.html (Links
to an external site.)Foot Locker in the Shoe MixFoot Locker, Inc., is the world's number one
retailer of athletic footwear and apparel. Headquartered in New York City, the
company has over 44,000 employees and 3369 retail stores in 23 countries across
North America, Europe, Australia, and New Zealand operating under such brand
names as Foot Locker, Lady Foot Locker, Kids Foot Locker, Footaction, Champs
Sports, and CCS. Foot Locker estimates that it controls about 18% of the U.S.
$15 billion athletic footwear market. The company intends to increase its share
of the worldwide market by adding additional stores and by growing its Internet
and catalog business.
In recent years, Foot Locker officials have
been rethinking the company's retail mix. Determining the shoe mix that will maximize
profits is an important decision for Foot Locker. By the year 2002, in an
effort to stock more lower-priced footwear, the company had reduced its
inventory of sneakers priced at $120 or more by 50%.
DISCUSSION
Suppose the data
presented below represented the number of unit sales (million $) for athletic
footwear in the years 2000 and 2012. Use techniques presented in this chapter
to analyze these data and discuss the business implications for Foot Locker.
Price Category
2000
2012
Less than $30
115
126
$30-less than
$40
38
40
$40-less than
$50
37
35
$50-less than
$60
30
27
$60-less than
$70
22
20
$70-less than
$85
21
20
$85-less than
$100
11
11
$100 or more
17
18
Suppose Foot Locker
strongly encourages its employees to make formal suggestions to improve the
store, the product, and the working environment. Suppose a quality auditor
keeps records of the suggestions, the persons who submitted them, and the
geographic region from which they come. A possible breakdown of the number of
suggestions over a 3-year period by employee sex and geographic location
follows. Is there any relationship between the sex of the employee and the
geographic location in terms of number of suggestions? If they are related,
what does this relationship mean to the company? What business implications
might there be for such an analysis?
Sex
Male
Female
U.S. West
29
43
U.S. South
48
20
Location
U.S. East
52
61
U.S. North
28
25
Europe
78
32
Australia
47
29
3.
16.1
The Financial
database contains seven different types of companies. These seven are denoted
by the variable Type. Use a chi-square goodness-of-fit test to determine
whether the seven types of companies are uniformly distributed in this
database.
4.
16.2
In the Manufacturing
database, is the Value of Industrial Shipments (a four-category variable)
uniformly distributed across the database?
5.
16.3
Use a chi-square
test of independence to determine whether Control is independent of Service
in the Hospital database. Comment on the results of this test.
6.
16.4
In the Consumer
database, is Location independent of Region? Use a chi-square test of
independence to answer the question.
2.
Click this link
http://www.physics.csbsju.edu/stats/contingency_NROW_NCOLUMN_form.html
Input '6' for number of rows and '2' for number of columns,
click 'submit', then you will see a new page with blank cells, type the data in
the given problem into those cells, then click 'Calculate now' to see the
results.
Interpret the
results.
For supplemental file, click on the following link: BUS6780_M5HomeworkAssignment
#2.docx
3.
Chapter 12 Case
Study (Caterpillar), pages 471-472, question 1 only. Use an alpha of
.05. You need to submit your supporting formula work or work in
Excel.
The United States Department of Agriculture
(USDA), in conjunction with the Forest Service, publishes information to assist
companies in estimating the cost of building a temporary road for such
activities as a timber sale. Such roads are generally built for one or two
seasons of use for limited traffic and are designed with the goal of
reestablishing vegetative cover on the roadway and adjacent disturbed area
within ten years after the termination of the contract, permit, or lease. The
timber sale contract requires out sloping, removal of culverts and ditches, and
building water bars or cross ditches after the road is no longer needed. As
part of this estimation process, the company needs to estimate haul costs. The
USDA publishes variable costs in dollars per cubic-yard-mile of hauling dirt
according to the speed with which the vehicle can drive. Speeds are mainly
determined by the road width, the sight distance, the grade, the curves and the
turnouts. Thus, on a steep, narrow, winding road, the speed is slow; and on a
flat, straight, wide road, the speed is faster. Shown below are data on speed,
cost per cubic yard for a 12 cubic yard end-dump vehicle, and cost per cubic
yard for a 20 cubic yard bottom-dump vehicle. Use these data and simple
regression analysis to develop models for predicting the haul cost by speed for
each of these two vehicles. Discuss the strength of the models. Based on the
models, predict the haul cost for 35 mph and for 45 mph for each of these
vehicles.
SPEED (MPH)
HAUL COST
12-CUBIC-YARD END-DUMP VEHICLE $ PER CUBIC YD.
HAUL COST
20-CUBIC-YARD BOTTOM-DUMP VEHICLE $ PER CUBIC YD.
10
$2.46
$1.98
15
$1.64
$1.31
20
$1.24
$0.98
25
$0.98
$0.77
30
$0.82
$0.65
40
$0.62
$0.47
50
$0.48
$0.40
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