Mathematics and Statistics

Table of Contents

Vacation Histogram ……………………………………………………………………………………………………………….1

Means …………………………………………………………………………………………………………………………………2

Promotion Recommendation ……………………………………………………………………………………………………3

Bonus Recommendation …………………………………………………………………………………………………………4
Grievance Board …………………………………………………………………………………………………………………..5

Probability Table …………………………………………………………………………………………………………………..6

Promotions Committee …………………………………………………………………………………………………………..7

Evaluation Confidence Interval …………………………………………………………………………………………………8

T-shirt Order ………………………………………………………………………………………………………………………..9

The Issues to be Addressed

Issue 1

Nine employees need to be chosen randomly to serve on the Grievance Board from the Employee Roster so that no one will say that we chose employees based on popularity. You may use any method, including with the aid of a random number table, to accomplish this task. However, you have to explain your method, whichever you choose to use.

Please list the employees ID# after selecting them.

Issue 2

Please complete the following two conditional probability tables. There have been complaints that there is skewness in certain departments as it relates to ethnicity and gender. It seems that certain supervisors are hiring only females or only Asians. Please complete this accurately so that the CEO can see if there are hiring trends in his agency.

Table I
White Black Hispanic Asian Foreign Total
Dept. 1
Dept. 2
Dept. 3
Dept. 4
Dept. 5
Total

Table II
Female Male Total
Black
White
Hispanic
Asian
Foreign
Total

Issue 3

Please create a histogram for vacation hours for employees in Department 1, 3, and 5. Please exclude any vacation hours over 320 as a person cannot accumulate vacation over that amount.

After you have created this histogram, please indicate the distribution’s shape.

Issue 4

Find the Mean weight for Departments 4 and 5 combined.
Find the Mean salary for Department 2.
Find Mean age for Department 1.
Find the Mean Placement Score (P. Score) for Department 3.

Issue 5

Find the standard deviation for the evaluation score (E. Score) of Department 5 and Department 2 separately.

The CEO is thinking about giving one of these department a $1000 per person bonus. Based on their means and standard deviation, which department is doing better as it relates to this year’s evaluation? Who should the bonus go to and why?

Issue 6

The Equal Opportunity Commission has cited Jordan & Associates with discrimination against Asian females and Hispanic females. They need to promote either an Asian female or an Hispanic female within the next month. Based on their evaluation scores (E. Score), find the corresponding z -score for each Asian and Hispanic female and make a decision on which person should be promoted. Please list them by their ID # based on the percentile.

Use = 6.06 and = 16.

Issue 7

Please refer to the conditional probability table or complete it first before attempting this assignment. The CEO has asked for a committee to be formed to approve and review promotions. Please list all your answers in percentages?

From Table 1, what is the probability of choosing an African American employee?

From Table 2, what is the probability of choosing an Asian female given all females?

From Table 1, what is the probability of choosing a White employee from Dept. 2 and then an Hispanic employee from Dept. 3?

From Table 2, what is the probability of choosing a Black male or Foreign male?

From Table 1, what is the probability of choosing a Foreigner or an Hispanic both from Department 5?

Issue 8

Find the evaluation score (E. Score) confidence intervals for the following two departments: Department 1 and Department 4 combined.

Find the confidence interval at the 95% level. Use s = 6.06 and = 17.625

Issue 9

We are about to order the annual summer picnic T-shirts. In the past, the mean employee weight is 210 lbs with an s = 67 lbs. Test H a> 210 at 0.05 significance level by combining the weights of departments 2, 3, and 4. If their mean weight is greater than 210, we need to order all extra large T-shirts. Please make a decision.
Use these data to answer the nine issues cited above.
The Data
ID #
Dept.
Ethnicity
Gender
Weight
Age
Salary ($)
Vacation Hrs.
Absences
E. Score
P. Score

694
3
F
F
252
18
69,380
300
16
24
94

261
3
W
F
178
21
39,986
60
22
22
90

138
2
B
F
132
21
40,000
138
34
15
86

222
2
B
F
162
22
32,000
159
32
17
76

556
5
B
M
219
24
31,000
120
70
19
98

300
1
W
F
192
24
84,000
120
18
18
80

58
3
H
F
110
25
12,775
60
0
14
94

169
1
W
M
138
26
25,594
125
0
21
72

558
5
F
M
220
27
22,000
85
7
16
87

765
4
F
M
271
30
22,697
330
42
17
71

728
3
B
F
270
30
97,424
60
16
22
65

901
2
W
M
310
31
18,000
1292
40
15
71

611
5
W
F
229
31
98,000
85
15
13
84

264
1
H
F
189
31
67,089
125
81
20
70

128
2
B
M
127
31
48,000
444
10
15
91

118
1
W
M
126
31
37,328
85
61
25
84

101
2
A
F
124
32
66,000
336
47
21
96

605
3
H
F
226
34
27,082
60
24
10
76

945
5
W
F
399
35
14,000
120
15
8
75

721
4
H
M
255
35
31,466
64
9
18
80

852
1
F
M
288
37
51,243
85
40
1
72

207
3
A
F
159
37
54,101
300
49
15
79

811
5
W
M
287
38
35,000
325
43
10
86

508
5
F
M
217
38
17,000
300
45
7
77

927
4
W
M
315
41
40,718
212
15
15
97

17
4
F
F
97
41
83,331
534
28
11
88

421
5
H
M
212
42
11,000
60
78
1
92

327
2
W
F
204
43
214,000
317
90
23
74

507
4
W
M
215
44
43,847
58
0
12
80

204
3
H
M
151
46
80,712
150
34
12
80

325
3
B
F
198
47
86,274
150
17
17
82

206
1
W
F
155
47
15,544
85
85
18
94

333
2
H
M
210
48
26,400
384
0
19
79

727
4
W
M
262
51
15,155
156
0
19
81

496
2
B
F
214
51
15,400
155
39
11
77

233
4
A
M
174
53
29,050
151
0
25
76

971
1
F
M
407
56
43,761
120
21
23
85

301
4
W
M
195
59
73,582
564
110
23
97

877
1
A
M
290
66
12,484
85
28
16
87

906
5
B
F
314
73
91,000
325
12
22
73

 

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