Unformatted Attachment Preview
Option 1: Springdale Shopping Survey
Instructions
The major shopping areas in the community of Springdale include Springdale Mall, West Mall, and the downtown
area on Main Street. A telephone survey has been conducted to identify strengths and weaknesses of these areas
and to find out how they fit into the shopping activities of local residents. The 150 respondents were also asked to
provide information about themselves and their shopping habits. The data are provided in the file SHOPPING. The
variables in the survey can be found in the file CODING.
The contingency tables and relative frequency probabilities in this exercise are based on the Springdale Shopping
Survey database. Information like that gained from the two parts of this exercise could provide helpful insights into
the nature of the respondents, their perceptions, and their spending behaviors. In particular, part 2 focuses on how
conditional probabilities related to spending behavior might vary, depending on the gender of the respondent.
Note: Be sure to use five (5) decimal places for your probabilities in the report, as some of them will be quite small.
Do not convert to percentages as we are interested in probabilities only here.
1.
Based on the relative frequencies for responses to each variable, determine the probability that a
randomly selected respondent from:
A. SPRSPEND [variable 4] spends at least $15 during a trip to Springdale Mall.
B. DOWSPEND [variable 5] spends at least $15 during a trip to Downtown.
C. WESSPEND [variable 6] spends at least $15 during a trip to West Mall.
Comparing the preceding probabilities, rank the areas from strongest to weakest in terms of the
amount of money a shopper spends during a typical shopping visit.
2.
Based on the relative frequencies for responses to each variable, determine the probability that a
randomly selected respondent from:
A. BSTQUALI [variable 11] feels that Springdale Mall has the highest-quality goods.
B. BSTQUALI [variable 11] feels that Downtown has the highest-quality goods.
C. BSTQUALI [variable 11] feels that West Mall has the highest-quality goods.
Comparing the preceding probabilities, rank the areas from strongest to weakest in terms of the
quality of goods offered.
3.
Set up a contingency table for the appropriate variables given, and then determine the following
probabilities:
A. SPRSPEND and RESPGEND [variables 4 and 26]: Given that the random
respondent is a female, what is the probability that she spends at least $15
during a trip to Springdale Mall? Is a male more likely or less likely than a female
to spend at least $15 during a visit to this area?
B. DOWSPEND and RESPGEND [variables 5 and 26]: Given that the random
respondent is a female, what is the probability that she spends at least $15
during a trip to Downtown? Is a male more likely or less likely than a female to
spend at least $15 during a visit to this area?
C. WESSPEND and RESPGEND [variables 6 and 26]: Given that the random
respondent is a female, what is the probability that she spends at least $15
during a trip to West Mall? Is a male more likely or less likely than a female to
spend at least $15 during a visit to this area?
Based on the preceding probabilities, rank the shopping areas where males and females are most likely to least likely
to spend $15 or more during a shopping visit.
Paper Requirements
Write a report that uses the Written Assignment Requirements under the heading Expectations for CBU. Items that
should be included, at a minimum, are a title page, an introduction, a body which answers the questions posed in the
problem, and a conclusion paragraph that addresses your findings and what you have determined from the data and
your analysis. As with all written assignments, you should have in-text citations and a reference page. Please include
any tables of calculations, calculated values, and graphs associated with this problem in the body of your assignment
response.
Note: You must submit your Excel file with your report. This will aid in grading with partial credit if errors are found
in the report.
Springdale Shopping Survey*
The major shopping areas in the community of Springdale include Springdale Mall, West Mall, and the downtown
area on Main Street. A telephone survey has been conducted to identify strengths and weaknesses of these areas
and to find out how they fit into the shopping activities of local residents. The 150 respondents were also asked to
provide information about themselves and their shopping habits. The data are provided in the file SHOPPING. The
variables in the survey were as follows:
A. How Often Respondent Shops at Each Area (Variables 1–3)
1.
Springdale Mall
6 or more times/wk.
4–5 times/wk.
2–3 times/wk.
1 time/wk.
2–4 times/mo.
0–1 times/mo.
2.
Downtown
3.
West Mall
(1)
(2)
(3)
(4)
(5)
(6)
(1)
(2)
(3)
(4)
(5)
(6)
(1)
(2)
(3)
(4)
(5)
(6)
B. How Much the Respondent Spends during a Trip to Each Area (Variables 4–6)
4.
Springdale Mall
$200 or more
$150–under $200
$100–under $150
$ 50–under $100
$ 25–under $50
$ 15–under $25
less than $15
5.
Downtown
6.
West Mall
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(1)
(2)
(3)
(4)
(5)
(6)
(7)
8.
Downtown
9.
West Mall
(5)
(4)
(3)
(2)
(1)
(5)
(4)
(3)
(2)
(1)
(1)
(2)
(3)
(4)
(5)
(6)
(7)
C. General Attitude toward Each Shopping Area (Variables 7–9)
7.
Springdale Mall
Like very much
Like
Neutral
Dislike
Dislike very much
(5)
(4)
(3)
(2)
(1)
D. Which Shopping Area Best Fits Each Description (Variables 10–17)
10.
11.
12.
13.
14.
15.
16.
17.
Easy to return/exchange goods
High quality of goods
Low prices
Good variety of sizes/styles
Sales staff helpful/friendly
Convenient shopping hours
Clean stores and surroundings
A lot of bargain sales
Springdale
Mall
Downtown
West
Mall
No
Opinion
(1)
(1)
(1)
(1)
(1)
(1)
(1)
(1)
(2)
(2)
(2)
(2)
(2)
(2)
(2)
(2)
(3)
(3)
(3)
(3)
(3)
(3)
(3)
(3)
(4)
(4)
(4)
(4)
(4)
(4)
(4)
(4)
E. Importance of Each Item in Respondent’s Choice of a Shopping Area (Variables 18–25)
Not
Important
18.
19.
20.
21.
22.
23.
24.
25.
Easy to return/exchange goods
High quality of goods
Low prices
Good variety of sizes/styles
Sales staff helpful/friendly
Convenient shopping hours
Clean stores and surroundings
A lot of bargain sales
(1)
(1)
(1)
(1)
(1)
(1)
(1)
(1)
(2)
(2)
(2)
(2)
(2)
(2)
(2)
(2)
Very
Important
(3)
(3)
(3)
(3)
(3)
(3)
(3)
(3)
(4)
(4)
(4)
(4)
(4)
(4)
(4)
(4)
(5)
(5)
(5)
(5)
(5)
(5)
(5)
(5)
(6)
(6)
(6)
(6)
(6)
(6)
(6)
(6)
(7)
(7)
(7)
(7)
(7)
(7)
(7)
(7)
F. Information aboutt the Respondent (Variables 26–30)
26. Gender: (1) = Male
(2) = Female
27. Number of years of school completed:
(1) = less than 8 years
(3) = 12–under 16 years
(2) = 8–under 12 years
(4) = 16 years or more
28. Marital status: (1) = Married (2) = Single or other
29. Number of people in household:
persons
30. Age:
years
Each respondent in this database is described by 30 variables. As an example of their interpretation, consider row number 1.
This corresponds to respondent number 1 and contains the following information.
Variable number 6 = 7. The
respondent usually spends less
than $15 when she
shops at West Mall.
Variable number 26 = 2. The
respondent is a female.
5556774441131111167765667232421
Variable number 1 = 5.
The respondent shops at Springdale Mall 2–4 times/month.
Variable number 19 = 7.
Respondent believes “high quality
of goods” is very important in
choosing a shopping area.
*Source: Materials for this case have been provided courtesy of The Archimedes Group, Indiana, PA. Data are based on actual responses
obtained to this subset of the questions included in the survey; town and mall identities have been disguised as well as a number of
responses were updated.
Option 1: Springdale Shopping Survey
Instructions
The major shopping areas in the community of Springdale include Springdale Mall, West Mall, and the downtown
area on Main Street. A telephone survey has been conducted to identify strengths and weaknesses of these areas
and to find out how they fit into the shopping activities of local residents. The 150 respondents were also asked to
provide information about themselves and their shopping habits. The data are provided in the file SHOPPING. The
variables in the survey can be found in the file CODING.
The contingency tables and relative frequency probabilities in this exercise are based on the Springdale Shopping
Survey database. Information like that gained from the two parts of this exercise could provide helpful insights into
the nature of the respondents, their perceptions, and their spending behaviors. In particular, part 2 focuses on how
conditional probabilities related to spending behavior might vary, depending on the gender of the respondent.
Note: Be sure to use five (5) decimal places for your probabilities in the report, as some of them will be quite small.
Do not convert to percentages as we are interested in probabilities only here.
1.
Based on the relative frequencies for responses to each variable, determine the probability that a
randomly selected respondent from:
A. SPRSPEND [variable 4] spends at least $15 during a trip to Springdale Mall.
B. DOWSPEND [variable 5] spends at least $15 during a trip to Downtown.
C. WESSPEND [variable 6] spends at least $15 during a trip to West Mall.
Comparing the preceding probabilities, rank the areas from strongest to weakest in terms of the
amount of money a shopper spends during a typical shopping visit.
2.
Based on the relative frequencies for responses to each variable, determine the probability that a
randomly selected respondent from:
A. BSTQUALI [variable 11] feels that Springdale Mall has the highest-quality goods.
B. BSTQUALI [variable 11] feels that Downtown has the highest-quality goods.
C. BSTQUALI [variable 11] feels that West Mall has the highest-quality goods.
Comparing the preceding probabilities, rank the areas from strongest to weakest in terms of the
quality of goods offered.
3.
Set up a contingency table for the appropriate variables given, and then determine the following
probabilities:
A. SPRSPEND and RESPGEND [variables 4 and 26]: Given that the random
respondent is a female, what is the probability that she spends at least $15
during a trip to Springdale Mall? Is a male more likely or less likely than a female
to spend at least $15 during a visit to this area?
B. DOWSPEND and RESPGEND [variables 5 and 26]: Given that the random
respondent is a female, what is the probability that she spends at least $15
during a trip to Downtown? Is a male more likely or less likely than a female to
spend at least $15 during a visit to this area?
C. WESSPEND and RESPGEND [variables 6 and 26]: Given that the random
respondent is a female, what is the probability that she spends at least $15
during a trip to West Mall? Is a male more likely or less likely than a female to
spend at least $15 during a visit to this area?
Based on the preceding probabilities, rank the shopping areas where males and females are most likely to least likely
to spend $15 or more during a shopping visit.
Paper Requirements
Write a report that uses the Written Assignment Requirements under the heading Expectations for CSU-Global
Written Assignments found in the CSU-Global Guide to Writing and APA. Items that should be included, at a
minimum, are a title page, an introduction, a body which answers the questions posed in the problem, and a
conclusion paragraph that addresses your findings and what you have determined from the data and your analysis.
As with all written assignments, you should have in-text citations and a reference page. Please include any tables of
calculations, calculated values, and graphs associated with this problem in the body of your assignment response.
Note: You must submit your Excel file with your report. This will aid in grading with partial credit if errors are found
in the report.
University/College Professor/Instructor
J.W. Blake
WWCC
K.R. Cunningham
R.H. Doughty
L.M. Edwards
W.H. Greiner
I.D. Jackson
O.P. Lawson
G.F. Nelson
A.F. Paul
D.K. Raulson
T.R. South
E.A. Thomas
C.F. Viney
F.E. Yousef
Totals
Number Students Taught Graduated Publications
1470
1455
422
2242
1883
923
2261
1899
513
2404
2356
1178
1721
1291
594
1571
1304
391
2869
2209
972
2329
2213
797
2967
2344
961
1467
1408
366
1103
971
291
2300
1978
495
208
206
89
1299
1143
446
EWCC
A.D. Blaise
I.A. Frank
S.D. Gundel
P.O. Hogan
W.M. Kraft
L.I. Luebbers
J.H. Nye
J.A. O'Dell
R.W. Pauly
K.G. Ross
D.S. Smith
J.P. Trost
M.M. Wall
Totals
849
2750
1927
1368
803
2734
1557
199
1778
1717
460
2156
248
790
2145
1599
1327
731
2379
1246
161
1458
1356
455
1940
226
324
901
416
571
241
1142
461
47
437
570
196
485
77
NWCC
D.H. Allen
T.G. Black
M.A. Carter
M.P. Drake
J.K. Elmsworth
P.T. Grey
C.R. Heines
D.R. Jones
B.M. Keith
G.H. Matheson
P.R. Neighbors
S.T. Orion
A.P. Tracey
Totals
316
2310
2062
2927
2685
800
1478
2389
2654
1629
2065
1801
2661
259
2148
1567
2810
2443
672
1168
2317
2309
1434
1549
1639
2395
109
1074
752
843
855
195
327
672
670
645
480
721
671
P(Graduated) Rank by P(G) P(Publications) Rank by P(P) P(P|G) Rank by P(P|G)
Sum of Ranks Overall Rank
A
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
41
B
C
D
E
F
SPRIFREQ DOWNFREQ WESTFREQ SPRSPEND DOWSPEND WESSPEND
5
5
5
6
7
7
4
6
6
6
7
7
6
5
6
7
7
7
6
4
6
5
7
7
4
6
3
6
7
6
5
5
4
7
6
7
5
4
5
6
7
7
4
5
4
5
7
7
3
5
2
4
5
7
5
6
6
7
7
7
6
4
6
7
6
7
5
4
5
7
7
7
6
3
5
6
6
7
4
6
5
6
7
7
4
5
2
5
6
7
6
4
6
7
7
7
6
5
6
7
7
7
6
4
5
7
7
7
6
5
6
6
6
7
3
5
6
6
7
7
5
4
5
7
7
7
5
6
5
5
7
7
5
5
5
6
7
7
6
4
3
7
6
7
5
4
6
5
7
6
6
5
5
7
7
7
5
6
6
4
7
7
3
6
5
6
6
7
5
3
2
5
7
6
6
4
5
6
7
7
6
5
6
6
7
7
6
4
4
6
7
7
6
3
4
7
7
7
6
5
5
6
7
7
4
5
6
7
7
7
5
4
5
7
6
7
2
6
4
4
7
5
3
4
5
7
6
7
3
6
5
5
7
5
6
6
5
6
6
7
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
82
A
B
C
D
E
F
4
4
6
4
5
5
5
3
4
4
5
2
6
5
3
3
4
2
5
3
1
5
2
1
5
2
4
4
1
4
4
6
4
3
6
4
5
1
1
1
3
6
4
3
6
6
2
2
6
3
6
6
3
2
3
6
5
5
6
6
3
2
5
4
6
6
5
5
4
1
6
6
4
3
5
5
6
3
6
1
5
2
4
4
6
5
6
3
5
5
3
4
2
3
6
2
6
4
5
4
2
4
5
4
2
3
1
3
5
5
3
1
5
2
1
3
1
6
6
2
4
5
3
5
6
7
5
6
6
6
6
5
1
4
3
3
1
5
2
2
5
7
7
1
2
6
7
1
2
3
2
3
4
6
5
7
6
6
2
7
2
7
6
2
7
6
5
5
6
7
6
7
4
1
3
7
7
2
6
2
3
7
4
3
1
6
3
7
7
2
5
5
1
6
5
7
5
3
5
4
5
7
2
2
3
3
3
7
6
7
4
6
7
1
5
2
6
3
2
4
6
2
7
7
6
4
4
3
7
5
3
4
2
3
3
5
3
2
3
6
2
5
6
6
1
4
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
123
A
B
C
D
E
F
6
2
6
4
4
4
4
5
4
5
3
6
1
4
2
2
6
6
6
2
2
5
5
6
6
4
5
3
3
2
3
4
5
5
6
3
5
4
5
3
3
2
1
3
3
4
4
4
6
2
2
5
6
4
5
3
5
6
5
4
1
5
4
1
6
6
6
5
5
6
4
5
4
5
3
5
5
4
4
3
4
6
5
2
5
3
3
2
6
5
2
4
1
6
5
2
5
3
6
6
6
4
5
5
5
6
6
5
6
4
4
3
4
4
5
4
6
6
6
5
3
6
5
7
5
6
6
3
3
3
2
7
3
4
5
1
1
5
2
7
4
5
4
7
5
3
4
6
5
7
7
7
5
7
7
7
6
6
7
4
4
6
5
6
7
2
5
7
4
2
4
4
2
6
2
4
5
2
1
7
7
6
6
7
6
5
7
5
6
7
7
7
7
6
7
6
6
7
7
7
5
5
7
5
6
3
1
3
7
1
7
7
2
1
2
4
3
6
6
7
5
7
5
5
6
5
5
4
6
6
6
7
7
5
5
7
7
7
7
7
7
7
5
7
7
7
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
A
B
C
D
E
F
1
4
4
5
5
5
4
5
3
5
5
2
5
5
5
5
4
1
5
6
2
5
4
6
3
3
6
6
6
5
6
6
5
3
5
5
4
3
6
6
4
5
6
3
5
5
1
5
4
3
3
5
6
4
6
1
6
6
5
6
2
5
3
1
4
6
4
5
3
3
4
6
3
1
2
5
5
4
5
5
4
4
6
4
6
4
5
5
7
4
5
6
7
7
6
5
4
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7
4
5
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7
5
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7
6
7
4
7
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6
7
5
7
4
5
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7
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6
6
4
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7
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5
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5
7
7
7
7
5
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6
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6
4
6
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7
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6
7
4
5
G
1
2
3
4
5
6
7
8
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10
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41
H
I
J
K
L
M
SPRILIKE DOWNLIKE WESTLIKE BSTEXCHG BSTQUALI BSTPRICE BSTVARIE
4
4
4
1
1
3
1
5
4
3
1
1
3
1
5
3
4
3
4
4
1
2
4
3
4
2
4
1
3
3
3
1
1
1
1
5
5
3
1
1
3
1
4
2
4
1
1
3
1
4
3
3
2
2
3
1
5
4
4
3
2
3
1
4
4
3
1
1
1
1
3
3
3
4
4
3
1
3
4
3
1
2
3
1
3
4
3
4
1
3
2
3
2
3
4
1
4
1
4
3
4
1
1
3
3
4
3
2
1
1
1
1
4
4
4
4
1
3
1
4
4
3
3
1
3
1
4
4
3
1
2
3
1
4
3
1
1
1
2
1
4
3
2
1
4
4
1
4
3
3
4
1
2
1
5
3
4
1
1
3
1
2
5
4
2
2
2
1
4
3
2
1
1
3
1
4
4
4
1
1
2
1
4
3
3
1
1
3
1
4
4
4
1
1
3
1
4
4
5
1
1
1
1
3
5
3
4
2
3
1
4
4
3
1
1
1
1
4
4
4
4
2
3
1
5
3
3
1
1
3
1
3
3
2
1
1
3
1
4
4
3
4
1
1
1
4
5
4
2
2
2
2
5
3
4
1
1
3
1
4
3
3
1
2
3
1
3
2
1
1
1
4
1
4
4
4
3
2
3
1
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
82
G
H
I
J
K
L
M
4
5
3
4
4
4
4
5
1
2
1
1
1
5
1
4
1
2
2
1
5
1
3
3
4
2
4
5
4
2
1
4
4
1
3
2
4
4
2
3
2
3
5
5
2
3
4
4
1
3
4
1
1
3
3
4
5
3
2
3
5
1
5
5
2
3
4
1
4
3
2
1
3
1
5
5
2
4
5
4
4
3
4
5
3
4
3
4
3
4
1
4
5
2
2
2
4
2
5
5
4
3
3
1
5
1
5
2
3
4
4
2
3
5
2
2
5
5
3
3
1
5
1
1
1
2
1
2
3
4
4
1
1
2
1
3
4
2
3
2
4
1
3
3
3
2
2
2
1
3
3
4
3
2
3
2
2
2
4
4
1
2
3
3
1
1
2
1
2
1
2
1
3
3
3
1
2
2
2
1
1
1
1
1
4
1
2
3
2
2
1
2
4
1
3
1
3
1
4
2
1
4
1
3
2
3
3
2
3
3
3
4
4
1
3
4
3
2
3
4
1
3
2
1
2
2
4
2
4
2
4
3
3
3
3
3
1
3
3
1
1
3
2
1
1
2
1
1
2
2
2
1
4
1
3
2
1
3
1
4
2
4
3
3
4
3
2
1
2
4
3
1
1
1
2
4
3
1
4
1
2
1
3
4
3
2
4
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
123
G
H
I
J
K
L
M
4
1
5
2
2
5
3
4
3
4
4
3
1
2
1
4
5
4
5
5
5
4
4
4
4
4
4
5
4
5
4
5
4
5
5
5
5
4
4
4
4
1
1
4
4
2
1
5
5
1
3
3
5
2
3
3
3
4
3
4
3
3
4
3
4
4
2
3
3
3
3
3
4
5
3
4
4
4
4
4
5
3
3
4
5
4
2
5
4
1
4
5
5
1
4
2
2
2
3
3
4
3
3
4
5
4
5
3
1
4
4
1
4
4
3
4
2
2
3
3
2
1
1
2
3
4
1
2
3
2
4
4
4
4
2
2
1
3
4
1
2
3
2
2
4
2
2
1
1
4
4
4
1
1
1
1
3
4
1
1
1
1
1
1
2
3
3
2
4
4
2
4
4
2
2
1
3
2
4
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
2
1
1
2
1
4
2
1
4
2
4
4
3
3
1
1
3
2
4
4
1
3
3
3
3
3
3
2
3
3
1
3
3
3
3
1
3
3
1
2
2
3
3
1
3
3
3
3
1
1
3
3
2
2
3
1
3
2
1
4
4
4
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
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
G
H
I
J
K
L
M
4
3
5
4
3
4
4
3
3
5
5
5
5
5
4
3
4
4
4
5
5
5
5
1
4
5
5
3
4
3
2
3
4
3
4
4
3
5
4
3
1
3
3
5
4
3
5
4
4
5
4
5
3
3
2
5
1
3
4
3
5
3
4
4
3
2
5
3
4
4
5
3
2
2
4
4
4
5
2
1
4
4
3
3
1
1
1
4
4
4
3
3
1
2
1
1
3
3
3
2
1
4
3
4
1
1
1
2
1
1
4
2
1
1
1
2
4
2
4
1
4
2
2
1
1
1
2
1
1
2
3
1
1
1
1
2
2
2
1
2
3
1
3
3
3
3
3
1
4
2
2
3
3
3
3
2
3
3
3
3
3
3
3
3
1
1
4
3
1
1
1
1
4
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
2
N
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
41
O
P
Q
R
S
T
BSTHELP BSTHOURS BSTCLEAN BSTBARGN IMPEXCH IMPQUALI IMPPRICE
1
1
1
1
6
7
7
2
3
1
3
7
7
7
1
4
1
1
7
7
7
4
1
1
4
6
7
7
1
1
1
2
7
7
7
1
1
1
3
3
7
7
2
1
1
3
4
6
7
4
1
1
3
7
7
7
1
1
4
1
7
5
5
1
1
1
1
7
7
7
2
4
4
3
5
7
7
1
1
1
3
5
6
6
4
1
1
1
7
7
7
4
1
1
2
7
7
7
1
3
1
3
7
7
7
2
1
1
4
1
4
4
4
4
1
3
2
7
7
3
3
1
3
7
7
7
2
2
1
2
7
7
7
1
1
1
2
1
1
1
4
1
1
4
3
4
5
4
1
1
2
6
6
6
1
1
1
1
5
6
7
2
1
1
2
5
6
1
1
1
1
4
5
7
7
2
1
1
1
1
1
1
1
1
1
1
7
7
7
2
1
1
1
7
6
7
4
1
1
3
4
7
7
2
1
4
4
5
7
7
1
1
1
2
5
7
7
4
4
3
3
3
7
7
4
1
1
1
7
7
7
2
1
1
2
5
7
7
2
2
1
2
1
1
7
2
2
1
2
6
7
7
1
1
1
1
7
7
7
1
3
1
1
6
6
7
4
1
1
1
7
7
7
4
3
2
4
7
7
7
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
82
N
O
P
Q
R
S
T
4
1
2
1
2
2
4
4
4
3
4
1
2
1
1
3
4
2
2
1
3
4
2
3
1
1
4
1
2
1
1
2
1
3
4
1
3
1
1
1
4
1
1
2
1
1
1
1
1
3
4
1
4
3
2
1
4
4
1
4
3
1
3
4
2
4
2
2
1
2
1
3
3
3
4
2
4
4
2
4
4
3
1
1
2
1
1
1
4
1
2
1
3
3
2
2
3
2
1
4
2
3
2
2
3
1
3
4
4
3
4
4
4
3
3
1
1
2
4
2
2
3
4
3
3
2
1
3
2
4
1
1
1
3
4
3
3
2
1
3
2
2
4
2
1
1
3
3
3
3
2
4
3
4
4
3
1
4
4
3
4
4
2
4
4
7
3
6
7
5
1
6
5
4
4
6
5
3
2
7
3
4
7
2
5
7
4
2
5
7
5
2
2
5
4
1
7
1
2
7
2
4
4
1
5
7
7
7
5
6
7
7
7
2
6
7
3
7
2
4
3
3
2
4
7
6
1
2
4
4
7
3
4
4
5
7
1
3
7
2
7
7
5
6
4
1
7
7
7
7
7
7
7
7
1
3
1
3
4
2
7
2
2
4
3
1
1
7
3
6
7
5
5
1
6
3
5
6
2
4
7
1
3
4
2
4
2
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
123
N
O
P
Q
R
S
T
2
4
3
1
3
3
4
2
4
4
1
3
2
1
4
3
1
1
1
1
2
1
2
1
1
1
1
4
3
1
4
2
2
2
1
2
2
1
1
2
1
1
2
3
2
2
1
2
4
2
3
4
2
4
3
2
1
1
1
1
1
1
1
1
1
1
1
1
1
4
1
1
1
1
1
1
1
3
1
1
1
4
4
3
1
1
4
1
1
4
4
3
1
4
1
4
4
2
3
1
1
4
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
4
3
3
4
3
3
1
1
4
1
4
4
4
3
1
2
1
3
3
2
3
3
1
3
1
1
3
4
4
4
1
1
2
1
2
3
1
3
1
1
2
5
1
2
2
6
3
2
1
1
4
7
2
4
5
7
5
7
6
4
5
6
2
5
3
5
7
3
5
5
7
7
7
6
5
4
7
7
7
7
4
7
1
1
2
5
7
3
6
5
1
4
3
7
3
4
7
1
6
6
7
3
7
7
7
7
5
7
7
6
7
7
5
7
7
7
7
7
7
7
7
7
6
2
1
7
6
6
3
2
3
7
4
4
1
3
3
4
5
7
6
6
4
5
6
7
7
6
7
7
7
7
4
7
7
7
7
7
5
7
7
6
6
7
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
N
O
P
Q
R
S
T
1
1
1
4
4
1
4
1
4
2
1
1
3
3
3
1
1
1
1
1
1
1
1
2
4
1
3
2
1
1
3
4
4
1
3
4
1
1
3
1
1
3
3
1
1
3
2
1
1
1
1
3
1
1
1
3
1
1
1
4
1
1
1
1
4
1
1
1
1
1
3
1
1
1
1
1
1
1
1
2
4
1
1
2
3
1
1
1
3
2
3
1
1
2
2
3
1
3
3
2
3
3
2
3
1
1
2
3
1
1
3
3
7
6
7
7
1
1
7
7
5
6
7
7
6
2
7
3
7
2
7
6
7
7
5
7
7
3
3
7
7
7
7
7
4
1
5
7
3
7
7
7
6
6
6
5
6
7
7
7
7
7
7
7
7
4
7
7
3
7
7
7
5
7
7
7
4
7
7
5
7
7
7
6
7
7
7
7
7
4
7
7
7
5
7
4
U
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
41
V
W
X
Y
Z
AA
IMPVARIE IMPHELP IMPHOURS IMPCLEAN IMPBARGN RESPGEND RESPEDUC
6
5
6
6
7
2
3
7
7
7
7
6
2
3
5
4
5
3
7
1
3
6
6
5
6
7
2
3
7
7
7
7
7
2
3
6
5
6
5
6
2
3
5
3
6
4
5
2
1
6
7
7
7
7
2
3
7
6
7
7
6
1
4
7
7
7
7
7
2
4
5
5
4
4
5
2
3
5
5
6
6
7
2
1
6
4
4
6
5
2
3
7
7
7
5
6
2
3
6
4
6
3
6
1
3
6
2
3
4
1
1
3
6
4
3
3
6
2
4
7
4
4
3
6
2
3
7
5
6
6
5
2
3
1
1
1
1
1
2
3
4
6
4
4
5
1
4
6
5
7
6
7
1
4
7
2
5
3
6
2
3
1
6
1
6
5
1
3
6
6
5
6
7
2
3
2
3
2
4
3
1
3
5
5
4
7
4
1
3
6
6
6
5
6
1
3
5
5
7
7
7
1
3
6
4
2
3
5
2
3
5
5
4
4
5
1
3
6
7
6
6
6
2
3
7
7
7
5
7
2
3
7
6
5
5
6
2
3
7
6
7
2
7
2
3
6
6
3
5
6
1
3
7
7
7
7
4
2
3
3
5
5
7
4
1
4
7
4
7
7
7
2
4
7
4
7
7
7
2
2
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
82
U
V
W
X
Y
Z
AA
5
5
3
6
6
6
5
6
1
6
7
1
7
6
6
4
6
4
7
7
3
7
2
6
3
2
2
7
5
3
7
6
1
1
3
1
2
1
4
1
3
4
3
1
4
7
5
3
6
1
1
2
6
7
1
6
7
6
7
4
2
6
5
3
3
3
1
5
7
2
2
6
1
3
1
7
5
1
2
3
1
1
6
5
2
6
6
7
3
5
3
5
6
3
5
4
2
1
4
3
5
4
2
2
5
7
3
3
7
4
7
6
3
1
7
4
6
4
7
1
7
1
3
4
5
3
5
7
6
3
7
4
3
7
7
2
6
2
4
3
3
4
7
7
7
7
3
7
4
7
2
4
7
4
1
6
6
4
1
6
5
2
2
3
7
4
7
5
5
7
5
7
4
2
1
2
5
3
6
6
1
7
5
4
7
5
2
6
5
5
6
1
3
1
3
2
1
7
7
7
3
5
2
3
7
2
2
1
2
1
2
1
2
2
2
2
1
2
2
1
1
2
1
2
1
1
1
2
2
1
2
1
1
1
2
1
2
2
2
1
2
2
1
1
2
2
2
4
4
3
3
4
4
2
1
2
2
2
2
3
1
3
2
2
3
1
3
1
4
1
1
1
1
1
4
3
2
2
4
2
2
3
1
3
4
4
1
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
123
U
V
W
X
Y
Z
AA
3
1
6
3
2
2
4
7
1
3
6
2
2
4
5
7
7
7
7
3
7
7
6
6
5
5
6
4
6
4
5
7
6
7
4
7
4
7
5
7
7
2
3
7
2
7
2
2
3
5
6
1
7
4
2
7
3
7
6
6
1
6
5
4
2
3
6
7
4
7
7
6
7
6
7
3
6
1
6
7
5
7
1
2
5
6
7
2
3
6
7
6
3
5
2
1
1
6
7
6
6
1
6
3
6
5
4
6
5
7
5
6
6
7
6
5
6
7
7
7
6
7
6
2
6
7
3
3
6
3
6
7
6
5
3
1
6
4
4
6
6
7
1
6
6
5
5
5
7
6
6
5
7
6
7
6
5
4
7
2
7
7
6
5
5
3
3
6
3
7
5
7
1
6
1
3
7
2
4
5
7
6
6
4
6
6
7
5
7
5
6
7
6
1
6
5
6
4
6
5
7
4
7
6
6
1
1
2
1
2
1
1
1
1
2
2
2
2
2
1
1
1
2
2
2
2
2
2
2
2
2
1
1
1
1
1
2
1
2
1
1
1
2
2
2
1
1
1
2
1
1
4
1
2
4
2
2
1
1
4
3
3
1
2
2
3
2
2
3
2
2
2
2
4
3
4
3
2
3
3
3
4
2
4
2
3
4
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
U
V
W
X
Y
Z
AA
7
6
7
7
3
6
7
7
4
5
6
6
5
5
5
3
5
6
5
6
6
7
5
1
7
5
7
5
7
4
7
7
5
6
7
7
5
7
5
6
5
4
6
3
4
1
5
6
7
7
5
1
7
4
6
7
7
6
6
7
5
3
4
6
7
1
7
6
6
3
6
7
5
4
5
6
7
7
6
1
6
4
7
6
7
4
7
7
3
6
7
6
7
4
7
6
4
5
5
7
4
1
5
3
7
7
5
7
6
6
2
4
5
7
7
7
5
4
6
6
4
5
7
6
4
6
7
6
6
2
7
5
6
4
7
7
5
5
7
3
1
2
2
2
1
1
2
1
2
2
2
2
2
2
1
1
2
2
2
2
1
2
2
2
2
1
1
2
4
4
1
4
4
4
2
4
3
3
4
2
3
3
2
3
3
3
3
3
2
4
2
4
4
2
3
2
AB
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
41
AC
AD
RESPMARI RESPHOUS RESPAGE
2
4
21
2
5
21
2
5
18
2
7
20
2
4
19
2
2
19
2
4
19
2
1
20
2
2
44
2
3
29
2
4
20
2
6
17
2
5
19
2
4
20
2
4
21
1
1
20
2
1
23
2
5
18
2
4
20
2
6
17
1
1
24
2
2
21
2
3
19
2
1
18
2
1
20
2
4
19
2
2
21
2
4
19
2
5
21
2
4
20
2
3
19
2
5
21
2
3
19
2
4
19
2
8
18
2
3
28
1
3
41
1
4
37
1
2
24
1
7
49
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
82
AB
AC
AD
1
1
2
1
1
1
1
2
2
2
1
2
2
2
1
1
1
2
1
2
1
1
2
2
1
1
1
1
1
1
2
2
2
1
1
2
2
2
2
1
1
3
2
1
6
3
3
4
1
2
5
4
1
2
2
4
1
1
5
1
4
6
4
4
1
4
5
3
2
3
3
4
4
1
4
5
5
7
7
4
1
5
37
24
22
40
46
32
36
70
21
33
39
28
80
17
38
65
43
76
47
66
71
48
24
76
63
33
48
66
42
29
79
80
77
67
28
78
31
44
54
19
66
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
123
AB
AC
AD
1
2
2
2
1
1
2
2
1
2
2
2
2
2
2
1
1
1
2
2
1
2
1
2
2
1
2
1
2
2
2
1
2
1
2
1
2
2
1
2
2
6
1
4
3
1
1
6
2
2
2
2
2
7
1
4
3
3
2
3
2
4
2
4
1
1
4
1
3
3
1
1
2
1
4
6
6
3
1
7
5
3
61
49
64
79
55
64
53
63
51
35
52
51
40
40
43
30
35
24
31
26
27
18
29
66
20
27
22
25
19
21
65
66
24
32
20
59
27
27
42
21
28
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
AB
AC
AD
2
2
1
2
1
2
1
1
1
1
1
2
2
2
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
2
1
2
1
5
4
5
2
4
4
1
4
5
4
4
1
6
2
2
1
3
7
3
6
3
6
28
26
36
53
61
25
31
50
35
70
22
25
21
23
39
33
37
18
33
21
65
22
31
53
36
57
33
44