An American College conducted a study in the early 2000 to examine if there were any gender
Question:
An American College conducted a study in the early 2000 to examine if there were any gender pay gaps[1] in its four schools: Business, Health, Liberal Studies and Sciences. Data were collected of a sample of 199 academics on their annual salary, years of service, rank, school, gender and age. The data file: Faculty Salary (Research Report Dataset).xlsx is available on Blackboard. A small portion of the data is shown below:
Faculty ID | Age | Years of Service | Rank | School | Gender M/F | Salary ($/year) | ||
1 | 49 | 22 | ASST | BUSINESS | F | 106632 | ||
2 | 31 | 0 | ASST | BUSINESS | F | 80000 | ||
3 | 34 | 2 | ASST | BUSINESS | F | 114666 | ||
… | … | … | … | … | … | … | ||
Legend: There are three academic ranks in the dataset: ASST, ASSO and PROF, which stand for Assistant Professor, Associate Professor and Professor respectively.
Task 1 (Boxplots and t-tests)
(a) Construct separate boxplots of salaries for male and female academics, and compare their distributions (central location, spread and skewness).
(b) Test if male academics on average earn more than their female counterparts at 1%.
(a) Considering assistant professors only, test if male assistant professors on average earn more than female assistant professors at 1%.
(b) Considering associate professors only, test if male associate professors on average earn more than female associate professors at 1%.
(c) Considering professors only, test if male professors on average earn more than female professors at 1%.
Faculty ID | Age | Years of Service | Rank | School | Gender M/F | Salary ($/year) |
1 | 49 | 22 | ASST | BUSINESS | F | 106632 |
2 | 31 | 0 | ASST | BUSINESS | F | 80000 |
3 | 34 | 2 | ASST | BUSINESS | F | 114666 |
4 | 34 | 0 | ASST | BUSINESS | F | 112000 |
5 | 41 | 6 | ASSO | BUSINESS | F | 119962 |
6 | 28 | 0 | ASST | BUSINESS | F | 110000 |
7 | 58 | 23 | ASSO | LIBERAL STUDIES | F | 94376 |
8 | 52 | 22 | ASST | LIBERAL STUDIES | F | 83506 |
9 | 35 | 6 | ASSO | LIBERAL STUDIES | F | 81124 |
10 | 37 | 7 | ASSO | LIBERAL STUDIES | F | 75116 |
11 | 42 | 7 | ASSO | LIBERAL STUDIES | F | 83568 |
12 | 30 | 3 | ASST | LIBERAL STUDIES | F | 66958 |
13 | 57 | 23 | PROF | LIBERAL STUDIES | F | 111758 |
14 | 53 | 23 | PROF | LIBERAL STUDIES | F | 110750 |
15 | 26 | 0 | ASST | LIBERAL STUDIES | F | 74000 |
16 | 59 | 30 | ASST | LIBERAL STUDIES | F | 98926 |
17 | 39 | 4 | ASST | LIBERAL STUDIES | F | 66190 |
18 | 51 | 19 | ASSO | LIBERAL STUDIES | F | 95138 |
19 | 38 | 4 | ASST | LIBERAL STUDIES | F | 66190 |
20 | 54 | 21 | ASSO | LIBERAL STUDIES | F | 84870 |
21 | 43 | 17 | ASSO | LIBERAL STUDIES | F | 78460 |
22 | 35 | 0 | ASST | LIBERAL STUDIES | F | 56700 |
23 | 31 | 3 | ASST | LIBERAL STUDIES | F | 63666 |
24 | 41 | 6 | ASSO | LIBERAL STUDIES | F | 76908 |
25 | 31 | 1 | ASST | LIBERAL STUDIES | F | 62776 |
26 | 56 | 21 | PROF | LIBERAL STUDIES | F | 105900 |
27 | 43 | 18 | ASSO | LIBERAL STUDIES | F | 90310 |
28 | 48 | 20 | ASSO | LIBERAL STUDIES | F | 92424 |
29 | 49 | 21 | ASST | HEALTH | F | 95386 |
30 | 49 | 17 | ASSO | HEALTH | F | 87098 |
31 | 40 | 7 | ASSO | HEALTH | F | 74218 |
32 | 32 | 1 | ASST | HEALTH | F | 64800 |
33 | 37 | 4 | ASST | HEALTH | F | 71314 |
34 | 54 | 24 | PROF | HEALTH | F | 110770 |
35 | 32 | 3 | ASST | HEALTH | F | 66924 |
36 | 38 | 7 | ASSO | HEALTH | F | 74410 |
37 | 34 | 6 | ASST | HEALTH | F | 65700 |
38 | 28 | 3 | ASST | HEALTH | F | 70218 |
39 | 26 | 1 | ASST | HEALTH | F | 76900 |
40 | 35 | 2 | ASST | HEALTH | F | 70210 |
41 | 33 | 2 | ASST | HEALTH | F | 71088 |
42 | 40 | 8 | ASSO | SCIENCES | F | 78484 |
43 | 35 | 1 | ASST | SCIENCES | F | 66906 |
44 | 36 | 3 | ASST | SCIENCES | F | 69112 |
45 | 32 | 3 | ASST | SCIENCES | F | 71088 |
46 | 29 | 2 | ASST | SCIENCES | F | 73180 |
47 | 43 | 12 | ASST | SCIENCES | F | 82330 |
48 | 37 | 5 | ASST | SCIENCES | F | 70210 |
49 | 34 | 7 | ASSO | SCIENCES | F | 81432 |
50 | 34 | 8 | ASST | SCIENCES | F | 73332 |
51 | 35 | 9 | ASST | SCIENCES | F | 67200 |
52 | 41 | 6 | ASST | SCIENCES | F | 67328 |
53 | 39 | 11 | ASST | SCIENCES | F | 79646 |
54 | 44 | 17 | ASSO | SCIENCES | F | 98104 |
55 | 46 | 12 | ASST | SCIENCES | F | 73154 |
56 | 42 | 11 | ASST | SCIENCES | F | 68878 |
57 | 36 | 1 | ASSO | SCIENCES | F | 81000 |
58 | 43 | 18 | ASST | SCIENCES | F | 82190 |
59 | 51 | 19 | ASST | SCIENCES | F | 81286 |
60 | 51 | 16 | ASSO | SCIENCES | F | 87940 |
61 | 54 | 19 | ASST | SCIENCES | F | 85498 |
62 | 45 | 10 | ASST | SCIENCES | F | 72406 |
63 | 38 | 11 | ASSO | SCIENCES | F | 85848 |
64 | 39 | 8 | ASST | SCIENCES | F | 74332 |
65 | 50 | 19 | ASST | SCIENCES | F | 83946 |
66 | 33 | 2 | ASST | SCIENCES | F | 73180 |
67 | 44 | 11 | PROF | BUSINESS | M | 128750 |
68 | 37 | 7 | ASSO | BUSINESS | M | 127002 |
69 | 37 | 6 | ASSO | BUSINESS | M | 118852 |
70 | 45 | 20 | ASSO | BUSINESS | M | 98116 |
71 | 34 | 4 | PROF | BUSINESS | M | 189938 |
72 | 47 | 21 | ASST | BUSINESS | M | 109524 |
73 | 36 | 9 | ASSO | BUSINESS | M | 111032 |
74 | 44 | 18 | ASSO | BUSINESS | M | 91864 |
75 | 40 | 11 | ASSO | BUSINESS | M | 113742 |
76 | 31 | 5 | ASST | BUSINESS | M | 121770 |
77 | 29 | 2 | PROF | BUSINESS | M | 167266 |
78 | 37 | 2 | ASST | BUSINESS | M | 116000 |
79 | 40 | 14 | ASST | BUSINESS | M | 82550 |
80 | 44 | 10 | PROF | BUSINESS | M | 127282 |
81 | 45 | 17 | ASST | BUSINESS | M | 100212 |
82 | 33 | 7 | ASSO | BUSINESS | M | 116100 |
83 | 35 | 3 | ASSO | BUSINESS | M | 138842 |
84 | 49 | 22 | ASSO | BUSINESS | M | 115500 |
85 | 36 | 9 | ASSO | BUSINESS | M | 112988 |
86 | 32 | 6 | PROF | BUSINESS | M | 156614 |
87 | 33 | 5 | PROF | BUSINESS | M | 147728 |
88 | 59 | 24 | ASSO | LIBERAL STUDIES | M | 102856 |
89 | 47 | 21 | ASSO | LIBERAL STUDIES | M | 91430 |
90 | 59 | 27 | PROF | LIBERAL STUDIES | M | 112144 |
91 | 40 | 12 | ASST | LIBERAL STUDIES | M | 75096 |
92 | 47 | 14 | PROF | LIBERAL STUDIES | M | 102144 |
93 | 27 | 0 | ASSO | LIBERAL STUDIES | M | 78000 |
94 | 37 | 8 | ASST | LIBERAL STUDIES | M | 81016 |
95 | 41 | 16 | ASST | LIBERAL STUDIES | M | 74374 |
96 | 41 | 7 | ASSO | LIBERAL STUDIES | M | 103774 |
97 | 57 | 22 | ASST | LIBERAL STUDIES | M | 92682 |
98 | 29 | 0 | ASST | LIBERAL STUDIES | M | 65812 |
99 | 61 | 30 | PROF | LIBERAL STUDIES | M | 118512 |
100 | 59 | 24 | PROF | LIBERAL STUDIES | M | 119286 |
101 | 53 | 25 | PROF | LIBERAL STUDIES | M | 138838 |
102 | 54 | 19 | ASSO | LIBERAL STUDIES | M | 88126 |
103 | 47 | 22 | PROF | LIBERAL STUDIES | M | 112918 |
104 | 40 | 8 | ASSO | LIBERAL STUDIES | M | 80000 |
105 | 50 | 23 | PROF | LIBERAL STUDIES | M | 112008 |
106 | 36 | 7 | ASSO | LIBERAL STUDIES | M | 72828 |
107 | 51 | 18 | PROF | LIBERAL STUDIES | M | 94240 |
108 | 55 | 25 | ASSO | LIBERAL STUDIES | M | 99262 |
109 | 41 | 11 | PROF | LIBERAL STUDIES | M | 91164 |
110 | 59 | 24 | PROF | LIBERAL STUDIES | M | 110330 |
111 | 57 | 24 | PROF | LIBERAL STUDIES | M | 115032 |
112 | 55 | 22 | ASSO | LIBERAL STUDIES | M | 94506 |
113 | 27 | 0 | ASST | LIBERAL STUDIES | M | 63000 |
114 | 37 | 7 | ASSO | LIBERAL STUDIES | M | 75922 |
115 | 53 | 22 | PROF | LIBERAL STUDIES | M | 116014 |
116 | 34 | 0 | ASST | LIBERAL STUDIES | M | 63000 |
117 | 37 | 12 | ASSO | LIBERAL STUDIES | M | 83714 |
118 | 27 | 2 | ASST | LIBERAL STUDIES | M | 64892 |
119 | 30 | 0 | ASST | LIBERAL STUDIES | M | 63000 |
120 | 58 | 24 | PROF | LIBERAL STUDIES | M | 116878 |
121 | 58 | 25 | PROF | LIBERAL STUDIES | M | 140036 |
122 | 47 | 20 | ASSO | LIBERAL STUDIES | M | 93688 |
123 | 36 | 11 | PROF | LIBERAL STUDIES | M | 130566 |
124 | 33 | 8 | ASSO | LIBERAL STUDIES | M | 73170 |
125 | 62 | 28 | ASSO | LIBERAL STUDIES | M | 112672 |
126 | 35 | 6 | ASSO | LIBERAL STUDIES | M | 71940 |
127 | 49 | 21 | PROF | LIBERAL STUDIES | M | 105308 |
128 | 49 | 24 | PROF | LIBERAL STUDIES | M | 108416 |
129 | 59 | 25 | PROF | LIBERAL STUDIES | M | 112510 |
130 | 41 | 16 | PROF | LIBERAL STUDIES | M | 93914 |
131 | 39 | 8 | ASSO | LIBERAL STUDIES | M | 80002 |
132 | 46 | 16 | ASSO | LIBERAL STUDIES | M | 87362 |
133 | 32 | 7 | ASSO | LIBERAL STUDIES | M | 81968 |
134 | 53 | 25 | PROF | LIBERAL STUDIES | M | 134086 |
135 | 51 | 22 | PROF | LIBERAL STUDIES | M | 131962 |
136 | 57 | 25 | PROF | LIBERAL STUDIES | M | 108328 |
137 | 50 | 18 | ASST | LIBERAL STUDIES | M | 76948 |
138 | 59 | 24 | PROF | LIBERAL STUDIES | M | 116882 |
139 | 48 | 22 | ASSO | LIBERAL STUDIES | M | 98082 |
140 | 46 | 17 | ASST | LIBERAL STUDIES | M | 79104 |
141 | 50 | 23 | ASSO | LIBERAL STUDIES | M | 95618 |
142 | 56 | 25 | PROF | LIBERAL STUDIES | M | 114312 |
143 | 34 | 1 | ASST | HEALTH | M | 70876 |
144 | 48 | 20 | ASSO | HEALTH | M | 94694 |
145 | 53 | 20 | PROF | HEALTH | M | 108514 |
146 | 33 | 8 | ASSO | HEALTH | M | 95546 |
147 | 56 | 23 | PROF | HEALTH | M | 127950 |
148 | 30 | 1 | ASST | HEALTH | M | 70876 |
149 | 47 | 16 | PROF | HEALTH | M | 109672 |
150 | 34 | 7 | ASST | HEALTH | M | 71776 |
151 | 55 | 20 | PROF | HEALTH | M | 98176 |
152 | 55 | 23 | PROF | HEALTH | M | 131104 |
153 | 51 | 22 | ASST | HEALTH | M | 90222 |
154 | 51 | 23 | ASSO | HEALTH | M | 112980 |
155 | 33 | 2 | PROF | HEALTH | M | 216676 |
156 | 54 | 26 | ASST | HEALTH | M | 111170 |
157 | 37 | 2 | ASST | HEALTH | M | 73988 |
158 | 53 | 21 | ASSO | HEALTH | M | 113858 |
159 | 53 | 21 | ASSO | HEALTH | M | 93740 |
160 | 46 | 17 | ASSO | HEALTH | M | 92314 |
161 | 31 | 2 | ASST | SCIENCES | M | 68998 |
162 | 28 | 0 | ASST | SCIENCES | M | 70400 |
163 | 58 | 24 | PROF | SCIENCES | M | 107188 |
164 | 34 | 8 | ASSO | SCIENCES | M | 80462 |
165 | 43 | 8 | ASSO | SCIENCES | M | 74336 |
166 | 32 | 6 | ASST | SCIENCES | M | 68016 |
167 | 42 | 17 | PROF | SCIENCES | M | 96036 |
168 | 30 | 3 | ASST | SCIENCES | M | 76796 |
169 | 52 | 18 | PROF | SCIENCES | M | 106422 |
170 | 63 | 28 | PROF | SCIENCES | M | 137980 |
171 | 37 | 2 | ASST | SCIENCES | M | 70880 |
172 | 55 | 25 | PROF | SCIENCES | M | 116100 |
173 | 27 | 0 | ASST | SCIENCES | M | 68000 |
174 | 59 | 26 | PROF | SCIENCES | M | 126018 |
175 | 43 | 9 | ASSO | SCIENCES | M | 82836 |
176 | 50 | 21 | PROF | SCIENCES | M | 101558 |
177 | 61 | 29 | PROF | SCIENCES | M | 131302 |
178 | 55 | 23 | ASSO | SCIENCES | M | 107222 |
179 | 67 | 41 | ASSO | SCIENCES | M | 115342 |
180 | 34 | 6 | ASSO | SCIENCES | M | 84418 |
181 | 50 | 21 | PROF | SCIENCES | M | 93946 |
182 | 55 | 23 | PROF | SCIENCES | M | 110138 |
183 | 43 | 8 | ASSO | SCIENCES | M | 74478 |
184 | 53 | 25 | ASSO | SCIENCES | M | 102814 |
185 | 44 | 13 | PROF | SCIENCES | M | 119386 |
186 | 33 | 0 | ASST | SCIENCES | M | 69000 |
187 | 43 | 12 | ASST | SCIENCES | M | 82266 |
188 | 37 | 4 | ASST | SCIENCES | M | 71088 |
189 | 43 | 14 | ASST | SCIENCES | M | 78240 |
190 | 47 | 14 | ASST | SCIENCES | M | 89808 |
191 | 55 | 22 | PROF | SCIENCES | M | 108284 |
192 | 40 | 9 | ASST | SCIENCES | M | 100324 |
193 | 48 | 22 | ASSO | SCIENCES | M | 125832 |
194 | 47 | 14 | PROF | SCIENCES | M | 107322 |
195 | 41 | 12 | PROF | SCIENCES | M | 94672 |
196 | 49 | 14 | PROF | SCIENCES | M | 89460 |
197 | 37 | 11 | ASSO | SCIENCES | M | 84378 |
198 | 36 | 10 | ASST | SCIENCES | M | 72406 |
199 | 42 | 14 | ASSO | SCIENCES | M | 91458 |
Statistics The Art and Science of Learning from Data
ISBN: 978-0321755940
3rd edition
Authors: Alan Agresti, Christine A. Franklin