Question

Background

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%.

                                                                                                                                        (1 mark)

(a) Considering assistant professors only, test if male assistant professors on average earn more than female assistant professors at 1%.

(1 mark)

(b) Considering associate professors only, test if male associate professors on average earn more than female associate professors at 1%.

(1 mark)

(c)   Considering professors only, test if male professors on average earn more than female professors at 1%.

(1 mark)

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

Answer 1

		Values
Gender M/F	Rank	Count of Faculty ID	Sum of Salary ($/year)	Average
F	ASSO	20	1720790	86,040
	ASST	42	3229952	76,904
	PROF	4	439178	1,09,795
F Total		66	5389920	81,665
M	ASSO	47	4535666	96,504
	ASST	35	2804110	80,117
	PROF	51	6111310	1,19,830
M Total		133	13451086	1,01,136
Grand Total		199	18841006	94,678
b.
Total Salary of Male Faculty	134,51,086
No. Of Male Faculty	133
Average Salary of Male Professer	1,01,136
Total Salary of Female Faculty	53,89,920
No. Of Female Faculty	66
Average Salary of Female Professer	81,665
Male Academics Earns more then female average by	19,471
	24%
a.
Total Salary of Male Assistant Professor	28,04,110
No. Of Male Assistant Pro.fessor	35
Average Salary of Male AssistantProfessor	80,117
Total Salary of Female Assistant Professor	32,29,952
No. Of Female Assistant Professor	42
Average Salary of Female Assistant Professor	76,904
Male Assistant Professor Earns more then female average by	3,214
	4%
b.
Total Salary of Male Associate Professor	45,35,666
No. Of Male Associate Pro.fessor	47
Average Salary of Male Associate Professor	96,504
Total Salary of Female Associate Professor	17,20,790
No. Of Female Associate Professor	32
Average Salary of Female Associate Professor	53,775
Male Assistant Professor Earns more then female average by	42,729
	79%
c.
Total Salary of Male Professor	61,11,310
No. Of Male Professor	51
Average Salary of Male Professor	1,19,830
Total Salary of Female Professor	4,39,178
No. Of Female Professor	4
Average Salary of Female Professor	1,09,795
Male Assistant Professor Earns more then female average by	10,035
Note-
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