statistics_project_0 x
The Project
The infamous company,
Jordan & Associates, is in trouble again. The Deputy Director has just resigned in the midst of rumors going around the departments about discrimination, lawsuits, and even the company picnic has been canceled.
I would like to seek your help in putting together an Ad hoc Statistics Report to be submitted to the CEO so that he can make the appropriate corrective, proactive, and retroactive decisions for the troubled company.
The Report Format
As you might have known already, my brother, the Jordan & Associates CEO is a very difficult person: his way or the highway. He is also insistence on proper report format. Nonetheless, we have to address quite a few issues, which are listed in the later section. Meanwhile, please follow the standard Jordan & Associates report format as follow:
Make a cover page entitled:
Ad-hoc
Statistics Report submitted to the CEO. Then skip a few lines
By (Your Name)
Skip one or two more line and put the date.
This should be the first page, the cover. Then after the cover page, make a table of contents.
Write Table of Contents at the top center.
The table of contents should be listed as such:
Title Page ……………………………………………………………………………………………………………………………..i
Table of Contents ………………………………………………………………………………………………………………….iii
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 |
|||||||||||||
Table II
Female |
Male |
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 $1000 per person bonus. Based on their means and standard deviation, which department is doing better as it relates to this year’s evaluation? Who should the bonus go to and why?
Issue 6
The Equal Opportunity Commission has cited Jordan & Associates with discrimination against Asian females and Hispanic females. They need to promote either an Asian female or an Hispanic female within the next month. Based on their evaluation scores (E. Score), find the corresponding z -score for each Asian and Hispanic female and make a decision on which person should be promoted. Please list them by their ID # based on the percentile.
Use s = 6.06 and m = 16.
Issue 7
Please refer to the conditional probability table or complete it first before attempting this assignment. The CEO has asked for a committee to be formed to approve and review promotions. Please list all your answers in percentages?
From Table 1, what is the probability of choosing an African American employee?
From Table 2, what is the probability of choosing an Asian female given all females?
From Table 1, what is the probability of choosing a White employee from Dept. 2 and then an Hispanic employee from Dept. 3?
From Table 2, what is the probability of choosing a Black male or Foreign male?
From Table 1, what is the probability of choosing a Foreigner or an Hispanic both from Department 5?
Issue 8
Find the evaluation score (E. Score) confidence intervals for the following two departments: Department 1 and Department 4 combined.
Find the confidence interval at the 95% level. Use s = 6.06 and
= 17.62
5
Issue 9
We are about to order the annual summer picnic T-shirts. In the past, the mean employee weight is 210 lbs with an s = 67 lbs. Test H a > 210 at 0.05 significance level by combining the weights of departments 2, 3, and 4. If their mean weight is greater than 210, we need to order all extra large T-shirts. Please make a decision.
The Data
ID # |
Dept. |
Ethnicity |
Gender |
Weight |
Age |
Salary ($) |
Vacation Hrs. |
Absences |
E. Score |
P. Score |
||||||||||||||||||||||||||||||||||||||||||||||
6 9 4 |
3 |
F |
25 2 |
1 8 |
69,3 8 0 |
300 |
16 |
24 |
94 |
|||||||||||||||||||||||||||||||||||||||||||||||
26
1 |
W |
1 78 |
21 |
39,9 86 |
60 |
22 |
90 |
|||||||||||||||||||||||||||||||||||||||||||||||||
1 38 |
2 |
B |
1 32 |
40,000 |
34 |
15 |
86 |
|||||||||||||||||||||||||||||||||||||||||||||||||
222 |
162 |
32,000 |
1 59 |
32 |
1 7 |
76 |
||||||||||||||||||||||||||||||||||||||||||||||||||
5 56 |
5 |
M |
2 19 |
31,000 |
1 20 |
70 |
19 |
98 |
||||||||||||||||||||||||||||||||||||||||||||||||
1 |
1 92 |
84,000 |
80 |
|||||||||||||||||||||||||||||||||||||||||||||||||||||
58 |
H |
1 10 |
25 |
12,7 75 |
0 |
14 |
||||||||||||||||||||||||||||||||||||||||||||||||||
169 |
26 |
25,594 |
125 |
72 |
||||||||||||||||||||||||||||||||||||||||||||||||||||
558 |
220 |
27 |
22,000 |
85 |
7 |
87 |
||||||||||||||||||||||||||||||||||||||||||||||||||
7 65 |
4 |
2 71 |
30 |
22,6 97 |
330 |
42 |
71 |
|||||||||||||||||||||||||||||||||||||||||||||||||
7 28 |
270 |
97,424 |
65 |
|||||||||||||||||||||||||||||||||||||||||||||||||||||
901 |
310 |
31 |
18,000 |
1292 |
40 |
|||||||||||||||||||||||||||||||||||||||||||||||||||
6 11 |
229 |
98,000 |
13 |
84 |
||||||||||||||||||||||||||||||||||||||||||||||||||||
2 64 |
189 |
67,089 |
81 |
20 |
||||||||||||||||||||||||||||||||||||||||||||||||||||
128 |
127 |
48,000 |
4 44 |
10 |
91 |
|||||||||||||||||||||||||||||||||||||||||||||||||||
118 |
126 |
37,328 |
61 |
|||||||||||||||||||||||||||||||||||||||||||||||||||||
101 |
A |
124 |
66,000 |
336 |
47 |
96 |
||||||||||||||||||||||||||||||||||||||||||||||||||
605 |
226 |
27,0 82 |
||||||||||||||||||||||||||||||||||||||||||||||||||||||
9 45 |
399 |
35 |
14,000 |
8 |
75 |
|||||||||||||||||||||||||||||||||||||||||||||||||||
721 |
255 |
31,4 66 |
64 |
9 |
||||||||||||||||||||||||||||||||||||||||||||||||||||
852 |
2 88 |
37 |
51,2 43 |
|||||||||||||||||||||||||||||||||||||||||||||||||||||
207 |
54,101 |
49 |
79 |
|||||||||||||||||||||||||||||||||||||||||||||||||||||
811 |
287 |
38 |
35,000 |
325 |
43 |
|||||||||||||||||||||||||||||||||||||||||||||||||||
508 |
217 |
17,000 |
45 |
77 |
||||||||||||||||||||||||||||||||||||||||||||||||||||
927 |
315 |
41 |
40,718 |
2 12 |
97 |
|||||||||||||||||||||||||||||||||||||||||||||||||||
83,331 |
534 |
28 |
11 |
88 |
||||||||||||||||||||||||||||||||||||||||||||||||||||
421 |
11,000 |
78 |
92 |
|||||||||||||||||||||||||||||||||||||||||||||||||||||
327 |
204 |
214,000 |
317 |
23 |
74 |
|||||||||||||||||||||||||||||||||||||||||||||||||||
507 |
215 |
44 |
43,847 |
12 |
||||||||||||||||||||||||||||||||||||||||||||||||||||
1 51 |
46 |
80,712 |
150 |
|||||||||||||||||||||||||||||||||||||||||||||||||||||
198 |
86,274 |
82 |
||||||||||||||||||||||||||||||||||||||||||||||||||||||
206 |
155 |
15,544 |
||||||||||||||||||||||||||||||||||||||||||||||||||||||
333 |
210 |
48 |
26,400 |
384 |
||||||||||||||||||||||||||||||||||||||||||||||||||||
727 |
262 |
51 |
15,155 |
156 |
||||||||||||||||||||||||||||||||||||||||||||||||||||
496 |
214 |
15,400 |
39 |
|||||||||||||||||||||||||||||||||||||||||||||||||||||
233 |
174 |
53 |
29,050 |
|||||||||||||||||||||||||||||||||||||||||||||||||||||
971 |
407 |
56 |
43,761 |
|||||||||||||||||||||||||||||||||||||||||||||||||||||
301 |
195 |
59 |
73,582 |
564 |
||||||||||||||||||||||||||||||||||||||||||||||||||||
877 |
290 |
66 |
12,484 |
|||||||||||||||||||||||||||||||||||||||||||||||||||||
906 |
314 |
73 |
91,000 |