Please enter your name:Exam Information:
The purpose of this Excel exam is to provide you with an opportunity to demonstrate what you have
Statistical Inference. You will be provided 6 questions, each with varying levels of difficulty. It is your
the best of your ability using only what you know and understand. You are ok to use your own person
course of your recent studies. You MAY NOT collaborate with others (this includes both current and p
members, etc.). You, and you alone, should be working on this assignment using only the previously m
You are encouraged to read the prompts provided and the questions that follow. Only answer the qu
necessary answer to meet the request of the question. For free response / fill in the blank questions,
answer to be submitted in. For questions that require tables and/or figures, space has been provided
completed, to the best of your ability, on the spreadsheet where questions are being answered. It is
spreadsheets, or you can copy the data set as is and include it on the spreadsheet where you are ans
remember is to ALWAYS show your work for these problems. Except in the case of a problem asking y
something, all questions can and should be answered using formulas, rather than hard coding numbe
demonstrate how an answer is achieved in order to receive partial credit. If there is no work, and an
received at all for said question.
All students are expected to know and follow the UH Academic Honest Policy. Any violations of the H
copying answers from another student, collaborating with other students on the exam/
exams, or discussing the exam with students who have not taken the exam (including
course and will be subject to disciplinary action.
Entering your name and PeopleSoft ID below indicates that you have read, understand
Name
This exam consists of 6 different questions, each with multiple parts, all worth a total of 55 points. Th
PLEASE FOLLOW ALL PROVIDED INSTRUCTIONS FOR A SMOOTH TEST TAKING
demonstrate what you have learned over the past few weeks concerning
g levels of difficulty. It is your responsibility to answer each of the questions to
are ok to use your own personal notes, textbook, and examples from the
is includes both current and past classmates, other professors, family
ent using only the previously mentioned tools.
at follow. Only answer the question as it is written, providing only the
e / fill in the blank questions, a dedicated box has been provided for your
ures, space has been provided for those as well. All your work should be
ons are being answered. It is ok to include cell references to the data set
readsheet where you are answering the question. The most important thing to
the case of a problem asking you to specifically filter, or if told explicitly to type
ather than hard coding numbers. Most importantly, though, is that you
it. If there is no work, and an answer is incorrect, then no credit will be
Policy. Any violations of the Honor Policy, including but not limited to
her students on the exam/questions, using copies of previous
aken the exam (including future semesters), will receive an F for the
ou have read, understand, and accept this Honor Statement.
PeopleSoft ID
worth a total of 55 points. There is also a separate 5 point bonus question.
FOR A SMOOTH TEST TAKING EXPERIENCE.
Maple Leaf Prints recently collected some data on magazine subscribers in an effort to better understand their customers. You
have been asked to provide support through the tasks that follow. To do so, please utilize the sample you’ve been provided, the
included templates, and the knowledge you have gained over the past few weeks to answer the following questions.
When utilizing the various templates, please copy the necessary data and specific template to the question tab. You can then complete all your
work on that specific tab (this is so you can use cell references rather than hard-coding values). Note that not every template might be used; it is up to you to
determine what is the appropriate test and/or confidence interval to apply for each situation.
Below you will find a data dictionary for the included data set. Please use this as a reference so you know the purpose each variable serves.
Description
Variable
Customer identification number.
CustomerID
Estimated income of customer.
Income
Total dollar amount paid for all magazine subscriptions over time.
TotalAmountPaid
MonthsSince1stOrder Receny (in months) of 1st order for this magazine; i.e., how long ago did the customer place their first order.
MonthsSinceLastOrder Recency (in months) of most recent order for this magazine; i.e., how long ago did the customer place their most recent order
Identifies the gender of customer. F = female, M = male.
Gender
Identifies the marital status of customer. S = single, M = Married, O = Other (divorced, widowed, etc.).
Marital
Identifies the type of residence. S = single family dwelling, M = multi family dwelling unit (apartment, etc.).
DwellingType
Indicates if children are present in the home. Y = child 21 or younger is present in the home, N = no child 21 or younger is in the
home.
ChildPresent
Identifies broad employment categories for customers. E = employed, H = at home (caregivers, homemakers, unemployed), R =
EmploymentStatus
retired.
Identifies the subscription status of a customer. A = active subscription, C = cancelled subscription, E = expired subscription.
MagazineStatus
Indicates whether the customer renewed their subscription while filling out this survey.
Renewal
Note: You have received a sample. So it is absolutely possible that a level listed above for your categorical variables might be missing. This is part of the risk
we take on with random sampling.
CustomerID Age
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
53
77
58
54
30
66
60
62
47
40
51
72
36
41
64
70
72
26
63
61
43
40
73
43
70
68
57
60
48
26
24
51
61
26
79
33
46
79
61
59
Income
TotalAmountPaid
MonthsSince1stOrder
MonthsSinceLastOrder
Gender
184000
37,94
266
22 F
62500
133,97
358
35 F
95000
35,97
123
123 M
62500
0
115
51 M
26000
38
131
118 M
88000
59
39
39 M
34000
140
40
40 M
32000
40
35
35 F
106000
55,97
122
122 M
72000
5
46
46 F
41000
33
109
109 F
54000
126,07
433
81 M
249000
19
157
138 F
22000
56,5
166
125 F
208000
65,94
126
70 M
29000
226,82
171
68 F
77000
40
113
65 M
137500
66
46
46 M
78000
20
106
106 F
51000
152,6
385
107 M
62000
19
121
121 F
174000
57,97
118
108 M
200000
44
96
96 M
42500
21,97
56
56 M
15000
22
85
76 M
12500
52,82
175
124 F
20000
20
102
102 M
87500
35,97
210
72 F
12500
123,95
160
123 M
5000
10
36
36 F
62500
94,91
186
120 F
226000
61,98
99
99 F
15000
23
42
42 M
126000
120
41
41 M
59000
102,02
246
96 F
21000
64
154
63 F
118000
96,97
192
84 M
113000
135
156
60 M
83000
46,5
114
75 M
41000
187,88
312
34 F
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
70
56
66
57
56
61
70
66
77
71
75
70
68
54
61
72
74
67
77
72
57
46
76
62
80
51
77
74
73
74
57
52
65
42
44
76
39
73
44
68
50
79000
24000
12000
144000
53000
46000
77000
119000
54000
70000
73000
137500
66000
93000
12500
55000
9000
5000
200000
149000
14000
11000
51000
5000
15000
54000
54000
152000
69000
28000
144000
148000
25000
141000
62500
5000
115000
27000
15000
30000
159000
182,97
219,77
68,76
122
40
183,83
0
29,49
177,88
42
20
146,97
31,96
0
102
82
199,97
29,17
84,94
195,96
89,82
36,01
137,77
5,99
37
105,41
49,99
78,04
70,92
245,91
122
12,97
163,35
82,97
113,97
45
22
93
66,5
78
44,5
288
324
57
246
93
240
45
517
126
404
312
118
102
32
32
120
66
174
155
262
76
169
348
65
130
106
164
193
99
273
246
89
203
192
72
28
105
83
118
286
250
42 F
113 F
57 F
32 M
93 F
75 F
45 M
22 F
63 F
62 F
111 M
118 F
102 F
32 M
28 F
80 M
66 F
33 M
99 F
36 M
76 F
80 F
142 M
65 F
114 F
105 M
76 F
120 M
99 F
34 F
32 M
76 F
135 F
128 F
72 F
28 F
105 F
70 F
118 F
100 M
50 F
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
68
78
70
54
52
52
40
46
54
55
37
38
66
27
53
72
65
78
75
49
69
35
66
55
66
56
49
67
34
30
30
37
74
38
76
64
62
54
54
58
77
21000
5000
15000
41000
112500
145000
207000
13000
183000
121000
170000
13000
31000
22000
118000
193000
79000
68000
5000
239000
98000
52000
13000
68000
31000
87500
147000
95000
112000
28000
67000
230000
66000
182000
51000
218000
30000
18000
5000
62500
49000
104,61
34
173
64,94
109,59
71,11
41
48,97
149,97
45,94
72
70
45
66
129,41
13,97
45,39
70
114,2
371,95
146,81
0
101
100,97
45
22
114,88
20
106,97
115,82
125,97
75
111
88,94
137,77
60
63
0
108
0
82,97
186
47
59
78
142
237
125
66
59
240
104
64
75
70
300
279
252
194
312
144
288
74
348
164
75
113
132
82
79
262
75
204
360
244
348
312
61
59
19
89
251
50 F
47 F
19 F
60 F
142 F
109 F
125 F
66 F
28 F
87 M
104 F
64 M
75 F
70 F
108 F
22 M
113 M
120 F
86 F
144 F
26 F
74 F
90 M
70 F
75 F
113 M
132 M
82 F
79 M
48 F
75 F
122 F
39 F
29 F
142 M
102 F
38 M
59 F
19 F
89 M
82 M
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
70
39
78
78
66
77
71
65
61
45
70
55
77
77
57
25
33
79
73
56
69
58
53
34
26
53
60
69
46
58
70
30
47
77
63
38
79
56
43
60
46
29000
115000
26000
50000
29000
64000
174000
26000
30000
355000
30000
101000
17000
40000
34000
129000
120000
35000
123000
30000
87500
212000
25000
137000
137500
13000
115000
31000
134000
42000
150000
122000
42000
10000
68000
90000
35000
51000
56000
115000
183000
50
19
270,89
239,92
20
22
175,95
42
22
115,97
247,92
88,94
44,97
183,94
54,45
62
43
19
179,39
158
164,04
44
10,48
66
66
61,94
50,87
33
40
404,71
86,88
4
0
38,97
78
13,97
19
98,96
20
50,87
22
118
124
276
421
102
262
275
39
105
165
421
336
139
115
37
64
16
57
185
113
68
146
117
67
46
238
71
109
100
235
216
35
45
60
51
126
57
45
51
71
31
89 F
124 M
20 F
63 M
102 F
23 F
24 F
39 M
105 M
141 F
88 F
81 M
86 F
115 F
37 F
56 M
16 F
57 M
107 F
89 F
68 F
77 F
114 M
67 M
46 M
131 F
71 M
109 F
93 F
65 M
81 M
35 M
45 F
60 F
51 M
41 M
57 M
45 F
51 F
71 M
31 F
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
74
54
40
72
78
64
64
61
42
63
63
44
72
36
57
69
45
47
40
49
65
71
65
75
68
49
70
60
65
54
71
43
78
49
73
69
68
153000
46000
83000
122000
119000
46000
183000
95000
11000
68000
50000
5000
193000
5000
42500
98000
200000
43000
18000
69000
37000
117000
25000
7000
42500
219000
15000
25000
30000
84000
54000
90000
87000
166000
48000
14000
12500
19,95
137,46
261,61
68
105
28,5
37
82,95
86,41
0
27
65,96
13,97
25,46
0,49
146,81
127,97
168,22
139,91
87,97
66
5
163,35
97,46
11,97
17
22
57,97
22
99,88
82,97
0
214,37
25
122,38
133,42
52,82
138
274
262
84
348
129
15
133
247
36
39
63
279
35
66
288
161
194
46
258
48
20
203
75
28
69
85
84
92
138
41
18
312
89
154
409
175
138 M
93 F
115 F
82 M
48 M
128 F
15 M
60 F
35 F
36 F
35 F
63 M
22 M
35 F
66 F
26 F
102 F
97 F
46 F
77 F
48 M
20 F
135 F
75 F
28 F
69 F
76 M
70 F
92 M
138 M
41 F
18 M
101 F
75 F
154 F
94 F
124 F
Marital
M
M
M
S
M
M
S
M
M
M
S
M
S
M
M
M
M
M
S
M
M
M
M
M
S
M
S
S
S
S
S
M
S
S
M
M
M
M
M
S
DwellingType ChildPresent MagazineStatus
Renewal
S
N
E
Yes
S
N
A
Yes
S
Y
C
No
M
Y
A
No
M
Y
C
No
M
N
E
No
M
N
A
No
S
N
E
Yes
S
Y
E
Yes
M
Y
E
No
S
N
C
Yes
S
N
C
No
S
Y
E
No
M
Y
C
No
S
N
E
No
S
Y
E
Yes
S
N
C
No
M
Y
E
Yes
M
N
E
Yes
S
N
A
No
M
N
C
No
S
Y
C
Yes
S
Y
E
No
S
Y
E
Yes
M
N
C
No
M
N
C
No
M
N
E
No
S
N
E
No
M
Y
C
No
M
Y
A
No
S
Y
C
No
M
Y
C
No
M
N
E
No
S
Y
E
Yes
M
N
E
Yes
M
Y
C
No
S
Y
E
Yes
M
N
E
No
M
N
C
No
S
N
E
Yes
EmploymentStatus
H
R
H
H
E
E
E
E
R
H
E
H
E
H
E
R
R
R
E
R
H
E
R
E
R
H
H
E
H
H
E
E
H
H
R
H
E
H
E
E
M
M
S
M
M
M
M
M
M
S
S
M
S
M
S
S
M
S
M
M
S
S
S
S
S
S
M
M
M
S
M
M
S
S
S
S
S
M
S
M
M
S
M
M
S
S
M
S
S
M
M
S
M
S
M
M
S
M
S
M
S
S
M
M
M
M
S
S
S
M
S
S
S
S
S
M
M
M
M
S
M
M
Y
Y
N
N
N
Y
N
N
N
N
N
Y
N
Y
N
N
Y
Y
N
N
N
N
N
N
N
Y
N
N
N
Y
N
Y
N
Y
N
N
Y
Y
Y
Y
Y
A
C
E
A
E
E
A
E
A
A
E
A
C
E
A
A
A
A
C
A
C
E
C
C
C
E
C
C
C
A
A
C
A
E
E
A
C
E
C
E
E
Yes
Yes
Yes
Yes
No
Yes
No
Yes
No
No
No
No
No
No
No
No
No
No
No
Yes
Yes
No
No
No
No
No
No
No
No
Yes
Yes
No
No
Yes
No
No
No
No
Yes
No
Yes
R
E
E
E
H
H
R
E
E
E
R
E
E
H
H
E
R
H
H
R
E
R
R
H
R
R
R
E
E
R
E
H
R
E
H
H
H
R
E
E
E
S
S
S
M
S
M
M
M
M
M
M
S
S
S
M
M
M
M
S
M
M
M
S
M
S
M
M
M
S
S
S
S
M
M
S
M
M
S
S
M
M
S
M
M
M
S
M
M
M
S
M
M
M
S
M
S
S
S
S
M
M
S
M
M
M
S
M
S
M
S
M
M
S
S
M
M
M
M
S
M
M
S
Y
Y
N
Y
Y
Y
Y
N
Y
Y
Y
Y
Y
Y
N
N
N
N
N
Y
N
Y
N
N
Y
N
N
Y
Y
Y
Y
Y
N
Y
N
N
Y
N
Y
Y
N
A
A
A
A
A
C
C
E
A
C
A
A
E
E
A
E
C
C
E
A
A
E
E
E
E
E
E
E
A
E
A
C
E
E
C
C
E
E
A
E
E
Yes
No
No
Yes
No
No
No
No
No
No
No
No
Yes
No
No
Yes
No
No
No
Yes
Yes
No
No
No
Yes
No
Yes
No
No
Yes
No
No
Yes
Yes
No
No
No
No
No
No
Yes
E
H
R
H
E
E
H
E
E
H
H
E
R
H
E
R
E
R
R
E
R
H
E
R
R
E
E
R
H
E
E
H
R
E
R
E
H
H
R
R
R
M
M
S
M
S
M
S
S
S
M
S
M
M
S
S
M
M
M
M
S
S
M
M
M
M
S
M
S
M
M
S
M
S
S
S
S
M
S
S
M
S
M
S
M
M
M
M
S
M
M
M
S
M
S
S
M
S
S
M
S
S
S
S
S
S
M
S
M
S
S
S
S
S
M
M
M
S
M
S
S
M
S
Y
Y
Y
N
Y
N
Y
Y
Y
Y
Y
Y
N
N
N
N
Y
Y
Y
Y
Y
N
Y
Y
Y
N
N
N
Y
N
N
N
Y
N
N
Y
Y
N
Y
N
Y
C
E
E
A
A
E
A
E
E
A
A
A
C
A
E
A
A
A
E
A
A
E
E
E
E
E
A
C
A
C
C
E
E
E
A
E
A
A
E
A
E
No
No
Yes
No
No
Yes
Yes
No
No
No
No
No
No
No
No
No
No
No
Yes
No
No
No
No
Yes
Yes
No
No
Yes
Yes
No
No
No
No
No
No
No
No
No
Yes
No
Yes
R
H
E
R
E
E
E
H
R
E
R
E
E
H
E
H
H
R
R
E
E
E
E
E
R
H
H
R
H
E
R
E
H
R
R
H
R
E
H
H
E
S
M
S
S
S
M
S
M
S
S
M
S
M
S
S
M
M
S
M
M
S
M
S
M
M
M
S
S
S
S
M
S
S
M
M
M
M
M
S
S
S
S
M
M
S
M
S
M
M
S
S
S
S
S
S
M
M
M
S
S
S
M
S
M
M
M
S
M
S
S
S
S
M
M
N
N
Y
N
Y
N
Y
N
Y
Y
N
Y
N
Y
N
N
Y
Y
Y
Y
Y
N
N
Y
Y
Y
N
Y
Y
N
Y
Y
N
Y
N
N
N
E
C
C
A
E
E
E
E
E
E
A
C
E
A
E
A
E
C
E
C
E
A
A
A
E
A
C
C
E
C
A
E
E
A
C
E
C
No
No
No
No
Yes
No
No
No
No
No
No
No
Yes
No
No
Yes
Yes
No
Yes
No
No
No
No
No
No
No
No
No
No
No
Yes
Yes
No
Yes
No
No
No
R
H
H
R
H
E
E
H
R
E
E
H
R
H
H
R
H
H
E
E
E
R
R
R
R
E
R
R
E
H
R
E
R
E
R
E
H
1 Before any statistical inference can occur, we should always get an idea of what our data look
like. This is known as exploratory (or descriptive) analysis. (worth 9 points)
a Please take the data and obtain the requested descriptive measures below for all numeric variables. The measures of interest are
provided. Please type the name of each variable on the row that says “Variable Name” and then calculate the corresponding
values. (worth 4.5 points)
Variable Name
Mean
Median
Standard Deviation
Kurtosis
Skewness
Minimum
Maximum
b Please build a frequency table for each categorical variable. The tables should list the names of each level of the variable and
their corresponding counts. CustomerID should be left out. Please place your tables below. DO NOT make one large
contingency table. You should have multiple smaller frequency tables that only contain information for each specific variable.
You will lose points for not following directions. (worth 4.5 points)
2 Our first order of business is analyzing the age of our customers. Maple Leaf Prints started out with
the goal of serving middle-aged to senior adults. Based on the sample that has been collected, is
there significant evidence to suggest the average age of subscribers has dropped below 60? (worth
10 points)
a What test should be performed here? (worth 1 point)
b What are your hypotheses for this test? (worth 2 points)
Parameter
Sign
Value
Null:
Alternative:
c What is the test statistic for this test? (worth 1 point)
Test Statistic:
d What is the p-value for this test? (worth 1 point)
p-value:
e What is your decision for this test? (worth 1 point)
Decision:
f If you rejected, at what significance level did you do so? (worth 1 point)
Significance level:
g Describe your result in terms of the problem. (worth 1 point)
h What is a two-sided 90% confidence interval for this parameter? (worth 2 points)
Lower Limit
Upper Limit
Please perform all your work over here. You can copy the necessary column(s) of data for your question and paste somewhere
below. It is your responsibility to make sure you correctly copy and paste the data. Missing information will result in you losing credit
for the question. Furthermore, please copy and paste the test and/or confidence interval template that you need for this question
along side the data. This will allow you to perform all your work in one centralized location, rather than having to continually
reference back to the data set and separate template.
3 Next, let’s check customers’ housing. Though many of Maple Leaf Prints’s customers are fairly
established, they still would like to keep a solid mix between those who have their own homes, and
those who stay in apartments/duplexes/etc. The company has tried to ensure that an equal number
of subscribers live in multi-family and single-family dwellings. Does the sample provide evidence to
suggest that the proportion of families that live in a multi-family dwelling is no longer 50%? (worth
10 points)
a What test should be performed here? (worth 1 point)
b What are your hypotheses for this test? (worth 2 points)
Parameter
Sign
Value
Null:
Alternative:
c What is the test statistic for this test? (worth 1 point)
Test Statistic:
d What is the p-value for this test? (worth 1 point)
p-value:
e What is your decision for this test? (worth 1 point)
Decision:
f If you rejected, at what significance level did you do so? (worth 1 point)
Significance level:
g Describe your result in terms of the problem. (worth 1 point)
h What is a two-sided 95% confidence interval for this parameter? (worth 2 points)
Lower Limit
Upper Limit
Please perform all your work over here. You can copy the necessary column(s) of data for your question and paste somewhere
below. It is your responsibility to make sure you correctly copy and paste the data. Missing information will result in you losing credit
for the question. Furthermore, please copy and paste the test and/or confidence interval template that you need for this question
along side the data. This will allow you to perform all your work in one centralized location, rather than having to continually
reference back to the data set and separate template.
4 Maple Leaf Prints is curious about the relationship between a customer’s job and whether or not
they keep their subscription to the magazine. The survey respondents have provided information on
what they do for employment, and the company was able to match that information with their
current subscription status. Do the data provide significant evidence to suggest that a customer’s
employment status is related to their subscription status? (worth 8 points)
a What test should be performed here? (worth 1 point)
b What are your hypotheses for this test? (worth 2 points)
Parameter
Sign
Value
Null:
Alternative:
c What is the test statistic for this test? (worth 1 point)
Test Statistic:
d What is the p-value for this test? (worth 1 point)
p-value:
e What is your decision for this test? (worth 1 point)
Decision:
f If you rejected, at what significance level did you do so? (worth 1 point)
Significance level:
g Describe your result in terms of the problem. (worth 1 point)
Please perform all your work over here. You can copy the necessary column(s) of data for your question and paste somewhere
below. It is your responsibility to make sure you correctly copy and paste the data. Missing information will result in you losing credit
for the question. Furthermore, please copy and paste the test and/or confidence interval template that you need for this question
along side the data. This will allow you to perform all your work in one centralized location, rather than having to continually
reference back to the data set and separate template.
5 Historically, the average customer has continued to place orders for about 6 years. Maple Leaf Prints
would like to check and see if this has changed based on the sample you have been provided.
Perform a test that checks whether the average duration of orders is now different from 6 years?
(worth 10 points)
a What test should be performed here? (worth 1 point)
b What are your hypotheses for this test? (worth 2 points)
Parameter
Sign
Value
Null:
Alternative:
c What is the test statistic for this test? (worth 1 point)
Test Statistic:
d What is the p-value for this test? (worth 1 point)
p-value:
e What is your decision for this test? (worth 1 point)
Decision:
f If you rejected, at what significance level did you do so? (worth 1 point)
Significance level:
g Describe your result in terms of the problem. (worth 1 point)
h What is a two-sided 99% confidence interval for this parameter? (worth 2 points)
Lower Limit
Upper Limit
Please perform all your work over here. You can copy the necessary column(s) of data for your question and paste somewhere
below. It is your responsibility to make sure you correctly copy and paste the data. Missing information will result in you losing credit
for the question. Furthermore, please copy and paste the test and/or confidence interval template that you need for this question
along side the data. This will allow you to perform all your work in one centralized location, rather than having to continually
reference back to the data set and separate template.
6 To get a better grasp on the types of customers Maple Leaf Prints has, as well as a better
understanding on what might cause a customer to stop their subscription, the company would like
you to compare renewal rates across customers based on whether the household has children or
not. Specifically, we are interested in testing if the renewal rate for households with children is
more than the rate those without. (worth 8 points)
a What test should be performed here? (worth 1 point)
b What are your hypotheses for this test? (worth 2 points)
Parameter
Sign
Value
Null:
Alternative:
c What is the test statistic for this test? (worth 1 point)
Test Statistic:
d What is the p-value for this test? (worth 1 point)
p-value:
e What is your decision for this test? (worth 1 point)
Decision:
f If you rejected, at what significance level did you do so? (worth 1 point)
Significance level:
g Describe your result in terms of the problem. (worth 1 point)
Please perform all your work over here. You can copy the necessary column(s) of data for your question and paste somewhere
below. It is your responsibility to make sure you correctly copy and paste the data. Missing information will result in you losing credit
for the question. Furthermore, please copy and paste the test and/or confidence interval template that you need for this question
along side the data. This will allow you to perform all your work in one centralized location, rather than having to continually
reference back to the data set and separate template.
Income
What shape do you see with the histogram?
Based on your test, do the data appear to come from a normally distributed population?
What is the average of these averages?
What distribution will you use to help you build the individual confidence intervals?
Place the histogram for the lower bounds here:
What is the average of these values?
Place the histogram for the upper bounds here:
What is the average of these values?
Out of 1000 95% confidence intervals, this number of intervals is expected to contain the true population average.
Number of intervals where the population average is between the lower and upper bound:
Percent of intervals where the population average is between the lower and upper bound:
Here is the data containing your 1000 samples of size 40. Please use these data w hen answ ering the questions related to bootstrapping.
sample
V1
V2
V3
V4
V5
V6
V7
V8
V9
V10
V11
V12
V13
1
101000 249000
11000
42500
18000
112000
62500
84000
87500
54000 200000
68000
29000
2
25000
14000
13000
42500
26000
95000
30000 226000 145000
30000
15000 122000
29000
3
34000 200000
62500
12500
12500
226000 144000
79000
90000 126000
5000 141000
53000
4
218000
30000
13000
59000 101000
249000
27000 174000
11000
10000
40000
20000
15000
5
30000
31000
27000 145000
46000
119000
54000
49000
62500 137500
79000
51000
5000
6
5000
46000
5000
11000 115000
120000
43000
15000
28000 112500
22000
83000 137500
7
46000
42000
70000
21000
14000
68000 239000 153000 117000
26000
5000
14000
62500
8
112000 239000
13000 193000
98000
22000
51000
95000
51000
5000
70000 147000 137500
9
170000 355000
37000
98000
83000
118000 137500
10000
55000
9000
68000
77000
5000
10
134000
7000 115000
88000
42500
150000
25000
31000
21000
68000
26000 121000
28000
11
51000 182000 118000 113000
22000
30000 152000
34000 134000
42500
51000
66000
13000
12
56000
84000
30000
29000
62500
93000
12500 193000
5000
30000
15000
42000
26000
13
41000 355000
26000 184000 121000
64000 159000 200000
20000
13000
31000
5000
12500
14
51000 226000
14000
40000 120000
54000
15000
31000
12500
41000
22000
12500
46000
15
144000
31000 249000
31000
53000
55000
87500
12000
11000
15000 137500
62500 170000
16
41000
13000
84000
26000 120000
62500
79000 117000 101000
34000
46000
12500
51000
17
25000
30000
87000 249000
51000
200000 112000
13000
62500 200000 152000
43000
31000
18
98000
68000
54000
32000
87500
12500
95000 174000 115000
42000
53000
42500
5000
19
55000
95000
84000
67000
95000
30000 193000 183000 119000
54000
69000
54000
21000
20
95000
49000 112000
14000
79000
141000
5000 153000
48000
59000
35000
54000 200000
21
54000
87500
90000
13000 150000
12500 193000
9000
11000 115000 170000
48000
69000
V14
119000
62000
51000
30000
50000
42000
183000
355000
121000
170000
30000
55000
87500
27000
18000
14000
5000
31000
77000
174000
145000
V15
35000
15000
123000
98000
174000
18000
68000
52000
144000
13000
41000
119000
18000
87500
49000
95000
153000
5000
70000
69000
20000
V16
207000
52000
24000
159000
13000
34000
207000
79000
62500
56000
48000
15000
30000
15000
95000
48000
52000
62000
5000
12500
118000
V17
62500
53000
37000
70000
5000
22000
174000
11000
212000
17000
69000
174000
31000
69000
43000
12000
42000
77000
159000
50000
112000
V18
5000
137500
115000
41000
40000
13000
18000
184000
218000
10000
30000
41000
14000
77000
54000
35000
18000
68000
93000
25000
18000
V19
150000
68000
35000
51000
218000
41000
5000
83000
21000
30000
18000
90000
30000
183000
52000
83000
54000
10000
230000
166000
29000
V20
5000
67000
93000
183000
15000
29000
208000
200000
30000
30000
29000
159000
149000
112500
95000
25000
148000
115000
14000
62000
43000
V21
137000
42500
152000
41000
137000
54000
115000
208000
183000
87500
25000
24000
78000
37000
5000
49000
193000
137000
11000
12500
119000
V22
34000
84000
10000
149000
115000
42500
26000
42000
28000
30000
62500
41000
77000
174000
166000
20000
15000
37000
5000
24000
56000
V23
93000
137500
29000
62500
30000
13000
159000
50000
90000
42500
12500
145000
41000
13000
30000
31000
54000
30000
73000
35000
137500
V24
5000
5000
54000
62500
70000
5000
184000
31000
41000
29000
79000
51000
25000
5000
30000
13000
144000
87500
25000
72000
37000
V25
149000
141000
15000
56000
77000
21000
152000
30000
26000
5000
112500
193000
87000
141000
153000
87000
79000
46000
64000
12000
123000
V26
14000
184000
87500
66000
68000
13000
88000
26000
182000
77000
37000
70000
95000
15000
183000
112500
34000
29000
87500
28000
144000
V27
25000
93000
106000
95000
29000
5000
62500
101000
15000
42000
5000
66000
24000
29000
12500
21000
9000
134000
13000
15000
42500
V28
153000
25000
56000
21000
42500
72000
25000
15000
193000
54000
239000
106000
239000
30000
69000
5000
66000
35000
25000
121000
21000
V29
55000
25000
42000
122000
137500
145000
24000
31000
145000
15000
54000
51000
69000
62500
41000
64000
20000
25000
5000
182000
30000
V30
144000
153000
46000
26000
22000
123000
12500
200000
54000
62500
46000
137500
12000
66000
22000
68000
5000
42500
355000
17000
54000
V31
9000
69000
54000
5000
30000
66000
5000
40000
30000
41000
5000
73000
30000
193000
9000
34000
78000
31000
43000
26000
101000
V32
22000
95000
115000
25000
5000
183000
87500
42000
34000
5000
137500
5000
46000
78000
118000
10000
25000
5000
12500
10000
106000
V33
69000
68000
218000
62500
5000
62500
30000
29000
26000
115000
31000
182000
68000
30000
35000
31000
17000
28000
15000
28000
42500
V34
5000
208000
35000
30000
73000
9000
137000
123000
129000
25000
119000
5000
50000
30000
35000
184000
62000
153000
9000
66000
15000
V35
5000
126000
27000
53000
13000
24000
137500
83000
46000
79000
159000
42500
120000
68000
62500
46000
26000
48000
87500
9000
32000
V36
212000
5000
66000
87500
87500
30000
123000
21000
93000
93000
137500
87500
141000
48000
112000
218000
159000
123000
115000
67000
34000
V37
144000
27000
137500
148000
87500
62500
30000
50000
5000
14000
84000
68000
193000
152000
137500
14000
115000
118000
21000
62500
249000
V38
35000
183000
9000
28000
134000
41000
87000
112500
123000
20000
15000
166000
83000
200000
137000
42500
149000
121000
226000
87000
129000
V39
15000
5000
115000
31000
51000
159000
212000
30000
84000
118000
41000
98000
62500
95000
42500
12500
5000
73000
148000
5000
5000
V40
90000
134000
5000
153000
93000
170000
54000
115000
24000
218000
87000
13000
26000
56000
115000
77000
14000
24000
153000
42000
30000
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
30000
42000
115000
50000
87500
15000
118000
5000
22000
41000
12000
5000
200000
118000
54000
95000
24000
26000
174000
95000
28000
166000
183000
42500
66000
5000
15000
66000
117000
12500
95000
95000
26000
239000
56000
25000
115000
129000
77000
170000
77000
12500
72000
68000
35000
137000
54000
15000
5000
153000
29000
29000
41000
152000
27000
5000
62000
30000
101000
72000
159000
30000
93000
43000
134000
13000
78000
30000
29000
200000
79000
84000
184000
144000
62500
119000
115000
48000
13000
126000
78000
20000
62500
84000
51000
170000
52000
78000
51000
5000
50000
34000
249000
67000
26000
115000
26000
5000
101000
193000
29000
35000
230000
90000
152000
212000
29000
32000
147000
87500
30000
193000
83000
207000
121000
55000
12500
122000
5000
79000
51000
53000
137000
50000
68000
5000
10000
62500
62500
13000
98000
119000
212000
87500
98000
126000
83000
83000
15000
11000
26000
141000
200000
183000
182000
112500
72000
12500
73000
166000
51000
12500
150000
5000
5000
12500
10000
42500
14000
62500
54000
17000
5000
122000
126000
26000
51000
43000
62500
62500
218000
13000
37000
26000
5000
28000
37000
40000
95000
78000
13000
141000
20000
30000
56000
43000
30000
77000
174000
41000
5000
79000
95000
87500
51000
212000
30000
193000
28000
5000
29000
49000
83000
208000
25000
115000
51000
119000
152000
30000
13000
219000
31000
88000
68000
15000
77000
134000
183000
51000
87500
137000
98000
21000
40000
18000
52000
46000
87500
193000
67000
226000
12000
126000
93000
5000
50000
62500
219000
62500
30000
5000
98000
115000
83000
29000
249000
54000
30000
30000
200000
183000
144000
90000
183000
42000
184000
54000
24000
183000
42500
182000
42000
15000
218000
62500
46000
166000
93000
12000
41000
25000
17000
27000
13000
145000
27000
25000
42500
35000
46000
120000
30000
62000
147000
11000
27000
95000
93000
30000
54000
87500
137500
52000
183000
31000
53000
41000
62000
226000
42500
34000
21000
112000
219000
87500
218000
148000
14000
87500
153000
15000
54000
5000
152000
28000
90000
249000
166000
13000
115000
55000
64000
207000
5000
193000
95000
79000
41000
29000
68000
21000
174000
200000
134000
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5000…
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