1. In R, use the commands given below to generate the following statistics of the variable that captures
the order fulfillment time. Write the answer and the full command used to generate the answer.
(0.5 points each)
a. min() (minimum):
b. max() (maximum):
c. mean() (mean):
d. sd() (standard deviation): ……other questions will be attahced
greaseburger__1_.pdf
s7_hw_pdf.pdf
Unformatted Attachment Preview
greaseburger (1)
id
store
burger chicken fries drink price ftime
1 Los Angeles
1
1
0
1 12.07
2 Los Angeles
1
0
1
1
9.87
95
3 Los Angeles
1
3
2
4 36.19
261
4 Los Angeles
3
1
0
4 27.41
231
5 Los Angeles
1
1
1
0 13.17
122
6 Los Angeles
0
0
2
0
6.58
71
7 Los Angeles
3
1
1
4
30.7
216
8 Los Angeles
2
2
3
5 40.57
294
9 Los Angeles
1
3
2
2 31.81
222
10 Los Angeles
1
1
0
2 14.26
122
11 Los Angeles
1
1
0
2 14.26
131
12 Los Angeles
1
1
1
2 17.55
146
13 Los Angeles
2
1
0
3 20.83
167
14 Los Angeles
1
0
0
0
4.39
80
15 Los Angeles
2
1
1
3 24.12
188
16 Los Angeles
1
1
2
2 20.83
158
17 Los Angeles
2
1
1
4 26.31
190
18 Los Angeles
5
3
1
7 57.02
414
19 Los Angeles
1
0
1
0
7.68
62
20 Los Angeles
2
2
0
4 28.51
269
21 Los Angeles
3
3
1
8 50.44
347
22 Los Angeles
1
0
0
2
8.77
104
23 Los Angeles
2
1
0
3 20.83
176
24 Los Angeles
1
1
1
2 17.55
159
25 Los Angeles
1
1
0
2 14.26
113
26 Los Angeles
1
1
3
1 21.93
153
27 Los Angeles
1
1
1
4 21.92
154
28 Los Angeles
1
3
0
6 33.99
262
29 Los Angeles
0
1
0
2
9.87
1
107
76
30 Los Angeles
1
3
2
4 36.19
268
31 Los Angeles
1
1
1
2 17.55
142
32 Los Angeles
1
1
0
0
9.88
140
33 Los Angeles
1
1
3
1 21.93
159
34 Los Angeles
1
1
1
0 13.17
118
35 Los Angeles
2
1
0
2 18.64
145
36 Los Angeles
2
1
1
3 24.12
182
37 Los Angeles
2
0
3
2 23.02
168
38 Los Angeles
1
0
3
0 14.26
118
39 Los Angeles
2
1
0
1 16.46
168
40 Los Angeles
1
1
2
2 20.83
178
41 Los Angeles
2
2
2
4 35.09
251
42 Los Angeles
1
1
1
2 17.55
172
43 Los Angeles
2
2
0
4 28.51
187
44 Los Angeles
1
0
2
1 13.16
119
45 Los Angeles
1
3
1
4
32.9
238
46 Los Angeles
2
0
1
3 18.63
172
47 Los Angeles
1
2
0
1 17.56
150
48 Los Angeles
1
1
1
2 17.55
170
49 Los Angeles
2
2
3
4 38.38
269
50 Los Angeles
2
0
1
3 18.63
108
51 Los Angeles
1
1
1
0 13.17
111
52 Los Angeles
0
0
1
0
3.29
15
53 Los Angeles
1
3
1
2 28.52
228
54 Los Angeles
1
3
1
4
32.9
286
55 Los Angeles
1
3
3
5 41.67
245
56 Los Angeles
1
1
1
1 15.36
152
57 Los Angeles
1
1
2
3 23.02
143
58 Los Angeles
1
1
0
3 16.45
177
59 Los Angeles
2
1
1
3 24.12
214
60 Los Angeles
1
1
2
3 23.02
154
61 Los Angeles
3
0
3
3
201
29.6
2
62 Los Angeles
1
1
4
4 31.79
212
63 Los Angeles
1
2
2
3 28.51
203
64 Los Angeles
1
5
0
7 47.16
401
65 Los Angeles
2
5
1
7 54.84
397
66 Los Angeles
1
3
1
4
32.9
234
67 Los Angeles
1
3
1
4
32.9
261
68 Los Angeles
2
1
1
3 24.12
190
69 Los Angeles
1
3
2
4 36.19
262
70 Los Angeles
0
2
1
2 18.64
152
71 Los Angeles
1
2
0
2 19.75
178
72 Los Angeles
2
0
0
2 13.16
98
73 Los Angeles
1
1
2
1 18.64
124
74 Los Angeles
1
2
0
3 21.93
214
75 Los Angeles
1
1
1
2 17.55
103
76 Los Angeles
0
3
0
3 23.03
191
77 Los Angeles
0
1
0
0
5.49
53
78 Los Angeles
1
0
2
1 13.16
112
79 Los Angeles
2
1
0
3 20.83
191
80 Los Angeles
4
1
2
5 40.57
244
81 Los Angeles
1
3
0
4 29.61
251
82 Los Angeles
2
2
0
4 28.51
222
83 Los Angeles
1
1
1
4 21.92
141
84 Los Angeles
1
1
2
0 16.46
96
85 Los Angeles
2
1
0
3 20.83
185
86 Los Angeles
1
1
1
0 13.17
117
87 Los Angeles
2
3
0
5 36.19
279
88 Los Angeles
1
2
1
3 25.22
212
89 Los Angeles
1
1
2
2 20.83
194
90 Los Angeles
1
0
1
1
9.87
90
91 Los Angeles
1
0
1
0
7.68
69
92 Los Angeles
1
1
2
3 23.02
200
93 Los Angeles
1
1
1
2 17.55
126
3
94 Los Angeles
0
1
0
0
5.49
52
95 Los Angeles
2
1
0
2 18.64
148
96 Los Angeles
2
2
1
4
31.8
287
97 Los Angeles
1
1
0
1 12.07
100
98 Los Angeles
1
0
0
1
6.58
85
99 Los Angeles
2
1
1
3 24.12
162
100 Los Angeles
1
1
0
4 18.63
130
101 Los Angeles
2
3
2
5 42.77
298
102 Los Angeles
1
0
1
1
9.87
119
103 Los Angeles
1
0
0
2
8.77
80
104 Los Angeles
5
3
0
8 55.92
418
105 Los Angeles
1
2
2
4
30.7
194
106 Los Angeles
1
1
2
3 23.02
163
107 Los Angeles
1
1
0
3 16.45
125
108 Los Angeles
1
1
0
2 14.26
122
109 Los Angeles
3
1
2
4 33.99
268
110 Los Angeles
1
1
2
1 18.64
145
111 Los Angeles
4
1
2
6 42.76
300
112 Los Angeles
2
1
2
2 25.22
194
113 Los Angeles
1
2
1
1 20.85
160
114 Los Angeles
1
1
0
2 14.26
100
115 Los Angeles
1
1
1
2 17.55
137
116 Los Angeles
1
1
0
2 14.26
132
117 Los Angeles
2
1
1
5
28.5
230
118 Los Angeles
1
1
2
0 16.46
130
119 Los Angeles
1
0
2
1 13.16
101
120 Los Angeles
1
1
3
1 21.93
194
121 Detroit
5
1
2
6 47.15 218.4
122 Detroit
1
5
1
5 46.07 243.6
123 Detroit
1
2
0
3 21.93 118.3
124 Detroit
1
2
1
2 23.03 134.4
125 Detroit
2
1
1
3 24.12 108.5
4
126 Detroit
1
1
1
2 17.55
93.8
127 Detroit
1
0
1
1
60.2
128 Detroit
1
2
1
2 23.03 142.8
129 Detroit
1
1
0
2 14.26
84
130 Detroit
1
1
3
2 24.12
126
131 Detroit
1
1
1
2 17.55
95.2
132 Detroit
1
1
0
2 14.26
78.4
133 Detroit
1
1
1
2 17.55 110.6
134 Detroit
1
2
2
3 28.51 141.4
135 Detroit
3
1
3
4 37.28 199.5
136 Detroit
1
1
2
3 23.02
126
137 Detroit
1
1
0
3 16.45
96.6
138 Detroit
1
1
0
2 14.26
96.6
139 Detroit
5
1
1
6 43.86 217.7
140 Detroit
1
0
1
1
141 Detroit
2
1
1
3 24.12 124.6
142 Detroit
1
1
1
2 17.55
143 Detroit
1
1
2
2 20.83 113.4
144 Detroit
1
3
5
4 46.06 224.7
145 Detroit
2
0
2
3 21.92
146 Detroit
1
0
1
1
9.87
49
147 Detroit
1
1
1
2 17.55
94.5
148 Detroit
2
0
2
3 21.92 105.7
149 Detroit
1
0
0
2
8.77
67.9
150 Detroit
0
0
2
0
6.58
47.6
9.87
9.87
5
70.7
70.7
98.7
Management 3: Quantitative Methods in Business
Session 7 – Assignment (20 points total)
Case Study: Greaseburger
Greaseburger is a relatively new but increasingly popular fast food brand. The chain is comprised of more than 2
dozen branches, primarily in urban and suburban locations throughout the country. Not surprisingly, most of Greaseburger’s
sales occur late at night, with peak sales generally observed around midnight. The quality of Greaseburger’s food has been
compared to chains such as Fatburger and In N’ Out, though customer sentiment within the fast food market is polarized, and
each brand is observed to have its own camp of staunch loyalists.
Because brand loyalty within this category is high, Greaseburger has struggled with how best to attract customers
who already have a preferred fast food brand. Management agrees that efforts to differentiate the brand on the quality of its
food alone have been unsuccessful, and for the past several months, the team has been actively exploring other ways of
helping the brand stand out in the late-night fast food market. One popular idea is to position Greaseburger as a more
convenient alternative to its competitors: while market research has indicated that Greaseburger’s competitors receive
consistently high ratings on the quality of their food, the same surveys have revealed another recurring theme: Greaseburger’s
competitors are plagued with long wait times and constantly crowded drive-through lines, much to the frustration of their
customers.
To capitalize on this opportunity, the marketing department at Greaseburger has proposed a new campaign in which
the company would offer to refund any order that takes more than 3 minutes to fulfill (‘fulfillment’ refers to the length of time
between the moment the order is placed and the moment the order is completed). Although the idea of the campaign has
sparked interest among the company’s top executives, management is rightfully concerned about the financial implications of
making such an offer, especially if the in-store operations at Greaseburger are not efficient enough to consistently satisfy the
time constraint. If fulfillment times are found to regularly exceed 3 minutes, the company risks exposing itself to some nontrivial
consequences: namely, the financial loss from refunding orders and the public relations fallout that would accompany the
necessary retraction of the campaign.
In order to explore the viability of the campaign, management has decided to conduct research into the current state
of the company’s in-store operations; specifically, they would like to know how likely it is that any given order will have a
fulfillment time of less than 3 minutes. While planning this research, an unfortunate shortcoming in the company’s order
tracking system has been revealed: currently, the system automatically logs the time at which the order is placed, but does not
log the time at which the order is completed, providing no way to immediately calculate the fulfillment time of past orders.
Management learns that implementing this new feature would be time consuming and very expensive; because the research
for the proposed marketing campaign is deemed time sensitive, the decision is made to proceed with the research now and
revisit the idea of building fulfillment time into the order tracking system at a later date. For the time being, management will
have to observe orders and manually record their fulfillment times.
The execution of the research is found to be quite simple, albeit a bit labor intensive. Two locations are chosen for the
initial phase of research: a branch in downtown Los Angeles, and a branch in a suburb of Detroit. At each branch, a
© Ryan Wagner, 2019. Do not copy or distribute without permission.
designated employee tracks one order at a time from start to finish. When a new order is placed, the employee starts a timer.
The moment the order is completed, the timer is stopped and the total time is recorded. This process is repeated at random
times throughout a shift. Some additional basic information about the order is also logged, including the composition of the
order and the total order price plus tax.
Currently, Greaseburger offers an extremely limited selection of items on its menu. Although the choice to offer a
limited menu was initially met with some resistance among the company’s executives, the strategy has been undeniably
successful: by limiting the menu to such a small number of items, management has been able to instead focus on ensuring the
highest possible quality of its ingredients, and has avoided the costs associated with supplying a wide variety of raw materials.
The current menu consists of a cheeseburger, a fried chicken sandwich, fries (one size), and a variety of fountain drinks.
Instructions: Download the file greaseburger.csv and import the file into R. The structure of the dataset is given below. For
each order, the following information is captured:
id
A unique identifier of the order
store
An identifier of the store at which the order was observed
burger
The number of cheeseburgers ordered
chicken
The number of chicken sandwiches ordered
fries
The number of fries ordered (in packages)
drink
The number of fountain drinks ordered
price
The total order price, including tax
ftime
The fulfillment time of the order in seconds
1. In R, use the commands given below to generate the following statistics of the variable that captures
the order fulfillment time. Write the answer and the full command used to generate the answer.
(0.5 points each)
a. min() (minimum):
b. max() (maximum):
c. mean() (mean):
d. sd() (standard deviation):
2. The following questions test the idea that orders are generally fulfilled in under 3 minutes.
a. By hand, generate a 90% confidence interval for the average fulfillment time in seconds (1 point)
b. Provide a verbal interpretation for your finding in part a (i.e., translate the numbers into words). How
does this finding support (or reject) the viability of the proposed marketing campaign? (1 point)
© Ryan Wagner, 2019. Do not copy or distribute without permission.
c. By hand, generate a 99% confidence interval for the average fulfillment time in seconds. (1 point)
d. How does your finding in part c support the viability of the proposed marketing campaign? Does it
strengthen or change your previous conclusion? (1 point)
e. Management is not thrilled with the lack of precision shown in the 99% confidence interval. Ideally,
they would like a margin of error of no more than 5 seconds on either side of the sample mean, with
the same level of confidence. Given the current sample statistics, how many orders would have to be
observed in order to achieve this? (1 point)
3. Below, write the R command to generate a table of the variable that shows the location at each order was
observed. In 1-2 sentences, comment on what you see in the table and its implications on the quality of the
data in this study, and provide a brief recommendation for how to improve data quality in any future iterations
of this research. (2 points – 0.5 point for R code, 1.5 points for written work)
4. Below, write the R commands to create two subsets of your data: one that contains only the observations for
the Los Angeles branch, and one that contains only the observations for the Detroit branch. Store each
subset as a new data frame with a name of your choice. (0.5 points each)
5. By hand, create two new 99% confidence intervals: one for the Los Angeles observations, and one for the
Detroit observations. You will need to generate the necessary summary statistics for each set. (2 points each)
6. Briefly comment on your findings in Q5 as they relate to the proposed marketing campaign. How does this
information relate to the recommendation you gave in Q3? (2 points)
7. After completing a second wave of research, management at Greaseburger finally receives a new batch of
sample data from participating branches. Management is pleased with the results: out of the 1,500 orders
observed, 1,319 reflected a fulfillment time of less than 3 minutes. Compute a 95% confidence interval for
the proportion of orders that have a fulfillment time of less than 3 minutes. (2 points)
8. In the post-mortem discussions about the research, the manager of the Detroit branch made the following
comment: “Yeah, tracking the fulfillment time was really simple, but it was really inconvenient to be without a
member of my staff because they were just standing by clicking a stopwatch. A couple of times when our
store got really slammed, I had to tell my employee to forget about the research and return to the assembly
line just so that we could keep things moving!”
In a few sentences, describe the potential implications of this manager’s actions on the quality of the
data collected. (2 points)
© Ryan Wagner, 2019. Do not copy or distribute without permission.
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