Question

2. (Lesson 11) The “Year” variable represents whether each student identified as a first-year student, sophomore,...

2. (Lesson 11) The “Year” variable represents whether each student identified as a first-year student, sophomore, junior, or senior. Use Minitab Express to conduct a chi-square test to determine if the proportions of students who identify as each year are not all equal. Use the five-step hypothesis testing procedure. [25 points]

Step 1: State hypotheses and check assumptions

Step 2:Compute the test statistic

Step 3: Determine the p-value

Step 4: Make a decision (reject or fail to reject the null)

Step 5: State a real world conclusion

Year
Senior
Sophomore
FirstYear
Junior
Sophomore
Sophomore
FirstYear
Sophomore
Junior
FirstYear
Sophomore
FirstYear
Sophomore
Junior
FirstYear
FirstYear
FirstYear
Sophomore
Sophomore
Sophomore
Sophomore
Sophomore
FirstYear
Sophomore
Sophomore
Sophomore
Sophomore
Junior
FirstYear
Senior
Junior
Sophomore
FirstYear
Senior
FirstYear
Sophomore
FirstYear
Sophomore
Sophomore
Junior
Senior
Sophomore
Sophomore
FirstYear
FirstYear
Junior
Senior
Sophomore
Senior
Sophomore
FirstYear
Senior
Junior
Senior
Junior
FirstYear
Junior
Sophomore
Sophomore
FirstYear
Sophomore
Senior
FirstYear
FirstYear
FirstYear
Sophomore
FirstYear
Sophomore
Sophomore
Senior
Senior
Sophomore
FirstYear
FirstYear
Sophomore
FirstYear
FirstYear
Sophomore
Sophomore
Sophomore
Sophomore
FirstYear
FirstYear
Junior
FirstYear
Sophomore
Senior
FirstYear
FirstYear
FirstYear
Sophomore
FirstYear
Sophomore
Sophomore
FirstYear
Sophomore
Sophomore
Sophomore
Sophomore
FirstYear
Senior
Sophomore
FirstYear
Sophomore
Sophomore

Sophomore
Sophomore
Sophomore
Sophomore
Sophomore
Sophomore
Sophomore
FirstYear
FirstYear
Sophomore
Sophomore
Sophomore
Sophomore
FirstYear
Sophomore
FirstYear
Sophomore
Sophomore
Sophomore
Sophomore
Sophomore
FirstYear
Sophomore
Sophomore
Senior
FirstYear
Sophomore
Sophomore
Sophomore
Sophomore
Sophomore
FirstYear
Sophomore
Junior
FirstYear
FirstYear
FirstYear
Junior
FirstYear
Sophomore
FirstYear
Sophomore
Sophomore
FirstYear
Sophomore
FirstYear
FirstYear
Sophomore
Senior
Sophomore
FirstYear
Sophomore
Senior
Sophomore
FirstYear
FirstYear
Sophomore
Senior
Sophomore
Sophomore
Junior
FirstYear
Sophomore
Sophomore
Sophomore
Sophomore
Junior
Sophomore
Senior
FirstYear
Sophomore
Sophomore
FirstYear
Sophomore
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Sophomore
Sophomore
Sophomore
FirstYear
Sophomore
Sophomore
Sophomore
Sophomore
Sophomore
Junior
Junior
Sophomore
Sophomore
Sophomore
Sophomore
Sophomore
Sophomore
FirstYear
FirstYear
Sophomore
FirstYear
Junior
Sophomore
Sophomore
FirstYear
Sophomore
FirstYear
Sophomore
FirstYear
Sophomore
Senior
Senior
Sophomore
Sophomore
FirstYear
Sophomore
Sophomore
Sophomore
Junior
Sophomore
Sophomore
Sophomore
Sophomore
Senior
Sophomore
Sophomore
Sophomore
Sophomore
FirstYear
Sophomore
Sophomore
Sophomore
Sophomore
Junior
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Sophomore
FirstYear
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Sophomore
Sophomore
Sophomore
FirstYear
Sophomore
Senior
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FirstYear
Sophomore
Sophomore
Sophomore
Junior
FirstYear
Sophomore
Senior
Sophomore
Sophomore
Junior
Sophomore
Sophomore
Sophomore
Sophomore
FirstYear

Junior
FirstYear
Junior
Sophomore
Junior
Sophomore
Sophomore
FirstYear
FirstYear
Sophomore
Sophomore
FirstYear
Sophomore
Senior
Senior
FirstYear
FirstYear
Sophomore
FirstYear
Senior
Sophomore
Sophomore
Sophomore
Senior
Sophomore
FirstYear
FirstYear
Sophomore
Sophomore
Junior
FirstYear
Sophomore
Sophomore
Senior
Sophomore
FirstYear
Sophomore
FirstYear
Sophomore
Sophomore
Sophomore
Sophomore
Sophomore
Junior
Junior
Sophomore
Sophomore
Senior
Sophomore
FirstYear
Junior
Sophomore
FirstYear
Senior
Sophomore
Sophomore
Senior
Junior
Senior
FirstYear
Senior
Junior
FirstYear
Sophomore
Sophomore
FirstYear
Sophomore
Junior
FirstYear
Junior
FirstYear
Junior
Sophomore
Sophomore
Sophomore
Sophomore
Sophomore
Sophomore
Sophomore
Senior
Sophomore
FirstYear
Sophomore
Sophomore
FirstYear
FirstYear
Senior
Sophomore
FirstYear
Sophomore
Sophomore
Senior
Junior
Sophomore
Sophomore
Sophomore
Sophomore
FirstYear
Sophomore

Gender
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Smoke
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Award
Olympic
Academy
Nobel
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HigherSAT
Math
Math
Math
Math
Verbal
Verbal
Math
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Verbal
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Math
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Verbal
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Exercise
10
4
14
3
3
5
10
13
3
12
12
10
12
6
9
10
3
7
2
14
10
14
20
7
12
10
6
14
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0
10
6
5
24
2
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6
5
5
12
2
7
15
5
7
15
8
14
14
4
15
4
15
3
3
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20
3
6
12
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15
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7
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15
4
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5
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2
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24
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3
20
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2
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1
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10
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18
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8
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12
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16
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8
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5
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10
7

15
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15
12
10
12
5
14
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12
15
3
25
5
6
27
8
3
17
40
5
0
27
3
3
11
2
9
12
15
2
20
12
5
10
2
12
5
3
12
8
8
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6
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10
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7
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4
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7
7
3
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14
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14
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2
1
15
5
5
15
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20
3
7
20
10
6
6
10
9
1.5
20
8
21
10
8
10
18
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5
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30
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2
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3
3
4
12
25
3
6
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7
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6
13
25
8
5
11
18
10
6
2
5
5
6
10
4
5
17
7
2
8
1
14
12

TV
1
7
5
1
3
4
10
8
6
1
6
5
8
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5
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5
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3
5
8
2
6
4
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2
20
10
2
5
5
5
5
5
5
4
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8
2
14
20
20
10
3
1
14
0
20
2
6
15
3
2
1
7
7
3
12
6
3
20
8
0
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6
4
4
6
5
3
3
8
8
20
5
4
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3
2
4
5
2
3
8
6
4
5
5
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8
2
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4
5
20
14
2
4
8
7
5
3
1
5
20
8
3
6
1
1
10
3
7
3
10
3
3
25
2
15
6
13
3
2
5
1
4
5
10
4
3
2
4
3
3
3
2
20
3
4
3
4
13
5
5
4
3
10
10
7
10
3
5
2
5
4
5
10
2
10
15
20
21
10
10
4
10
3
2
7
10
6
2
4
27
2
15
10
3
10
10
10
5
4
14
6
5
2
14
5
3
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2
5
2
10
3
40
10
14
4
2
7
2
5
15
5
12
4
0
15
0
6
5
10
3
16
9
2
5
6
12
1
0
2
10
1
14
2
10
7
2
5
7
20
4
1
8
2
5
6
5
2
4
2
20
2
1
10
3
4
3
14
10
10
3
0
5
5
2
2
5
4
2
3
4
5
9
1
7
6
6
5
4
5
20
3
5
1
2
14
3
0
5
0
10
10
15
1
3
6
20
28
3
1
5
12
1
7
6
5
2
3
4
4
5
4
5
5
10
4
5
1
5
14
10
15
5
3
20
5
3
3
2
5
4
6
8
2
2
2
4
8
12
5
6
5

14
1
25
3
25
10
1
4
2
10
0
10
1
5
5

Height
71
66
72
63
65
65
66
74
61
60
65
63
68
68
68
63
63
72
62
67
65
68
73
74
70
71
67
74
68
72
62
66
70
72
67
62
73
67
67
64
72
64
70
60
71
73
72
74
70
69
68
64
72
70
65
72
63
64
64
65
73
71
66
73
70
65
72
73
70
79
67
66
66
68
67
66
66
65
66
76
69
64
64
65
67
66
72
65
69
69
73
62
69
73
76
70
67
68
72
74
62
69
70
69
72
78
67
73
63
70

65
73
78
65
63
68
72
70
67
72
68
78
69
80
71
70
75
64
78
68
69
63
64
63
72
63
63
68
67
71
65
72
75
59
69
63
74
70
64
67
66
67
73
71
66
68
67
69
66
68
68
71
70
66
65
70
71
71
70
65
67
61
68
65
70
72
66
71
64
73
60
64
65
65
73
69
66
66
73
71
65
75
63
74
70
63
75
71
68
68
72
63
65
65
67
72
71
68
72
64
71
62
65
68
67
68
64
72
71
72
72
71
71
71
61
68
70
67
64
71
71
69
70
65
65
72
67
74

62
75
67
63
71
63
70
67
74
69
70
70
70
68
76
59
66
68
72
69

75
63
71
72
64
68
68
67
66
74
64

65
64
64
72
69
70
67
76
66
63
66
68
67
73
62
67
71
66
68
60
71
75
65
65
66
71
76
67
72
67
73
60
70
75
67
71

66
69
69
63
65
65
72
66
74
64
75
73
72
67
64
67
65
70
68
70
67
72
64
72
75
69
68
72
74

64
73
71
70
68
69

72
68
69
66
72
65
70
66
67
71
83
61
65
77
60

Weight
180
120
208
110
150
114
128
235

115
140
200
162
135
193
110
99
165
120
154
110
145
195
200
167
175
155
185
190
165
175
126
187
170
158
119
205
129
145
130
215
135
145
98
150
159
174
160
165
161
160
130
175
255
160
160
95
115
120
135
180
155
110
215
175
140
195
185
185
209
145
140
146
130
140
130
140
160
120
150
155
128
143
155
119
138
240
160
191
165
200
125
140
206
275
142
140
145
128
165
140
130
170
160
165
145
155
155
113
155
173
195
120
225
160
120
138
260
150
135
165
142
210
171
150
188
195
230
140
200
140
180
160
135
140
155
235
140
130
125
222
128
183
175
125
156
145
195
185
150
140
150
150
220
195
140
135
138
170
145
135
140
155
155
155
135
165
160
175
183
140
140
110
125
125
180
195
128
172
150
188
110
125
135
130
230
198
127
150
175
160
140
200
130
210
210
145
156
207
150
137
153
175
136
104
122
192
218
170
220
150
135
155
135
140
120
135
135
165
180
165
175
200
138
265
105
130
165
145
138
193
170
155
155
140
130
180
140
210
150
115
225
170
120
170
130
182
138
180
230
222
145
150
190
195
115
140
155
150
155
130
210
105
192
220
134
160
135
140
135
145
140

138

130
210
233
180
185
189
127
135
140
162
215
200
120
165
175
160
145
180
170
235
155
140
145
175
210
130
195
165
180
145
163
160
150
170
110
170
145
160
130
155

160
151
180
130
185
198
175
123
145
190
130
185
165
165
150
160
142
165
175
175
190
180
185

135
195
175
165
135
140
182
155
180
170
135
165
137
147
150
155
160
130
180
150
205
115

Siblings
4
2
2
1
1
2
1
1
2
7
1
2
3
2
1
1
2
2
1
1
1
8
3
1
1
3
1
1
1
1
2
5
3
2
4
1
1
1
0
0
3
2
0
2
1
1
1
1
1
1
2
2
2
2
4
0
0
2
1
2
1
0
2
2
2
3
2
2
2
1
3
1
1
2
1
1
1
3
1
1
1
3
2
2
2
1
1
1
3
5
2
1
2
1
1
1
6
5
1
1
1
1
3
2
2
1
1
3
1
1
1
2
1
2
1
2
1
2
2
3
1
3
6
1
4
3
0
2
2
1
0
5
1
3
2
2
5
3
2
5
1
3
2
0
1
1
3
4
2
1
0
1
0
1
2
1
2
1
2
1
2
0
2
1
1
2
1
2
1
3
2
1
2
0
2
2
2
3
1
1
1
2
1
3
2
2
1
1
1
3
3
2
1
1
3
2
4
3
0
1
2
2
2
3
2
3
1
1
4
2
1
4
1
1
1
1
3
1
2
1
2
2
1
0
1
1
3
1
1
1
2
1
1
1
2
1
3
2
1
0
1
3
2
0
1
2
1
1
2
0
2
4
1
0
3
1
1
1
2
2
2
3
3
1
3
1
1
1
1
0
1
2
2
2
2
2
2
1
6
1
3
1
1
0
2
0
2
1
3
2
2
1
3
1
2
1
3
2
2
2
1
1
1
6
1
2
1
1
3
3
1
2
1
1
1
1
2
1
1
2
1
1
2
1
1
0
2
4
1
3
2
1
3
1
0
2
1
2
1
1
3
1
0
1
1
1
2
1
2
1
3
2
0
2
1
2
2
1
2
2
2
0

BirthOrder
4
2
1
1
1
2
1
1
2
8
2
2

3
1
2
1
1
1
2
2
8
4
2
2
2
1
2
1
2
3
6
2
2
2
2
1
1
1

1
3
1
2
1
1
2
2
2
2
1
2
1
2
4
1
1
2
1
3
2
1
1
3
3
4
2
1
1
1
2
1
2
1
2
1
1
3
1
1
1
1
2
1
1
2
1
1
1
4
3
1
3
1
2
2
7
6
1
1
1
2
2
2
2
1
2
2
2
2
1
1
1
1
2
1
2
3
3
4
1
4
5
1
1
1
1
1
3
1
1
3
1
2
3
1
3
2
3
4
1
1
2
1
1
1
4
2
1
1

1
1
2
3
2
3
1
3
1
3
1
2
2
1
3
1
1
1
2
3
1
2
1
2
3
3
3
1
1
1
1
1
1
2
2
2
2
2
1
4
3
1
1
3
2
5
1
1
2
2
3
3
1
2
4
1
2
5
2
1
3
1
1
2
1
1
1
1
2
1
2
2
1
1
2
3
1
2
1
2
1
1
1
1
1
3
2
2
1
2
1
3
1
1
3
2
2
1
1
1
4
1
1
1
2
2
1
1
1
1
2
1
1
4
2
1
1
1
1
2
1
2
2
2
2
2
1
7
1
2
1
1
1
1
1
1
1
4
3
1
2
4
1
1
1
3
2
2
2
1
1
2
3
2
1
2
1
1
3
2
2
2
1
1
2
3
1
1
3
2
1
3
1
1
1
3
3
1
2
2
2
3
1
1
1
1
2
2
1
2
1
1
1
1
1
1
2
3
1
2
1
1
2
2
1
3
1
1
2
2
1

VerbalSAT
540
520
550
490
720
600
640
660
550
670
500
580
530
650
700
590
600
700
610
550
550
560
560
550
550
700
610
570
550
500
610
610
500
640
490
560
560
470
680
570
630
580
550
490
590
620
560
630
600
550
590
640
650
420
500
620
600
580
490
630
600
590
550
600
500
600
600
650
650
560
540
640
690
600
610
610
600
580
560
620
620
630
430
640
490
550
690
550
600
530
520
660
800
560
610
660
650
680
550
660
650
620
530
670
640
680
670
730
580
610
580
620
680
570
500
800
610
550
600
660
640
560
600
480
650
520
640
610
450
700
540
550
640
560
530
620
550
520
660
470
570
560
520
560
600
400
540
400
530
530
517
620
590
590
620
540
490
540
640
620
680
800
510
620
670
560
630
590
630
470
550
690
660
600
700
660
540
520
550
600
600
520
490
600
620
530
550
600
610
550
560
670
610
660
630
520
670
550
560
390
600
560
610
710
710
560
600
540
600
600
550
550
620
550
570
530
570
620
520
620
520
680
630
730
440
670
500
630
680
530
630
600
700
590
670
780
660
600
510
800
740
780
440
700
660
520
600
760
680
520
510
600
650
700
650
520
580
600
520
750
650
550
650
640
660
640
530
690
630
600
560
720
610
720
590
620
550
800
670
550
620
520
440
720
390
560
570
660
620
660
630
610
540
570
600
600
530
560
560
500
560
500
640
660
550
630
700
560
580
800
460
700
660
500
600
650
640
620
570
540
670
620
650
560
480
460
500
680
550
630
620
560
590
530
690
550
600
610
600
750
470
550
540
530
540
680
510
500
680
500
570
540
550
680
630
650
680
550
600
540
550
500

Homework Answers

Answer #1

Step 1: State hypotheses and check assumptions

H0: the proportions of students who identify as each year are all equal.

H1: Atleast one proportion of students who identify as each year are not equal

Step 2:Compute the test statistic

From Minitab Output

Test statistic Chisquare value = 188.689

Step 3: Determine the p-value

P-value = 0.000

Step 4: Make a decision (reject or fail to reject the null)

Here P-value < alpha 0.05 so we do not accept H0

Step 5: State a real world conclusion

Thus we conclude that  Atleast one proportion of students who identify as each year are not equal

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