Question

A personnel officer in a governmental agency administered four newly de- veloped aptitude tests to each of 25 applicants for entry-level clerical positions in the agency. For purpose of the study, all 25 applicants were accepted for positions irrespective of their test scores. After a probationary period, each applicant was rated for proficiency on the job. The scores on the four tests (Xi, X2. Xs, X4) and the job proficiency score (Y) for the 25 employees were as follows:

Subject Test Score Job Proficiency
Y
88
80
96
76
80
73
58
116
104
99
64
126
94
71
111
109
100
127
99
82
67
109
78
115
83 X1
86
62
110
101
100
78
120
105
112
120
87
133
140
84
106
109
104
150
98
120
74
96
104
94
91 X2
110
97
107
117
101
85
77
122
119
89
81
120
121
113
102
129
83
118
125
94
121
114
73
121
129 X3
100
99
103
93
95
95
80
116
106
105
90
113
96
98
109
102
100
107
108
95
91
114
93
115
97 X4
87
100
103
95
88
84
74
102
105
97
88
108
89
78
109
108
102
110
95
90
85
103
80
104
83

Answer 1

Following are the solution to these question:

Explanation:

Please find the complete question in the attached file.
`\text{Stem and leaf plot}\\\\\text{Stem-and-Leaf Display:}\ \ x_1\\\\\text{Stem-and-leaf of} \ \ x_1 \ N = 25\\\\`

`1 6 2\\3 7 4 8\\6 8 4 6 7\\10 9 1 4 6 8\\(7) 10 0 1 4 4 5 6 9\\8 11 0 2\\6 12 0 0 0\\3 13 3\\2 14 0\\1 15 0\\`

`\text{Stem-and-Leaf Display:}\ \ x_2\\\\\text{Stem-and-leaf of} \ \ x_2 \ N = 25\\\\`

`1 7 3\\2 7 7\\4 8 1 3\\6 8 5 9\\7 9 4\\8 9 7\\10 10 1 2\\11 10 7\\(3) 11 0 3 4\\11 11 7 8 9\\8 12 0 1 1 1 2\\3 12 5 9 9\\`

`\text{Stem-and-leaf of} \ \ x_3 \ N = 25`

`1 8 01 85 9 0 1 3 312 9 5 5 5 6 7 8 9(4) 10 0 0 2 39 10 5 6 7 8 94 11 3 42 11 5 6`

`\text{Stem-and-leaf of} \ \ x_4 \ N = 25`

`1 7 42 7 85 8 0 3 410 8 5 7 8 8 911 9 0(3) 9 5 5 711 10 0 2 2 3 3 45 10 5 8 8 91 11 0`