Wells and Associates is one of the largest financial counsulting firms in the Un
ID: 3351803 • Letter: W
Question
Wells and Associates is one of the largest financial counsulting firms in the United States. It provides lirancial advice and services to both private firms and state and local goveraments. It has 86 offices located in 42 states. There are six regional manugers who, with their staffs, supervise and support the local officers. Until three years ago, each region was operated as an almost com- pletely autonomous unit. The national office set revenue and service goals in conjunction with the regional managers and provided technical services, com- puter facilities, economic forecasts, and so forth Variable Number Number 2 F 37 1 9495 M22 24 27387 ·F 22 2927483 Three and a half years ago, the firm hired a managerment consulting firm in response to stable proits despite a continuing increase in total revenue. After six months of investigation, the consultants recommended a number of changes in the firm's operations. A consistent theme in these recommendations was the need for more centralization of routine tasks to increase both the effectiveness and efficiency with which they are performed. major 12 21 2.9 3 91 93 M232.5 3 6 64 19 In response to the consultants recommendations, a personnel division was established at the national headquarters to supervise all personnel matters including recruitment. Bill Koehler, who had been in charge of personnel in the largest regional ofice, was placed in charge of this department. Lori Muller who had just been placed in charge of the personnel departmen in the next-to smallest division, was named as his assistant. The department was also as signed four sccretaries. In the past three years, another assistant and two more secretaries have been added. Six wees ago, the department added a newly gradeated statistician M 22 243 50 0 F 22 23 85 77 M 21 22 2 52 F 25 32 3 83 4 M 23 223 0 30 M 21 238 7 1 24 232 77 66 Lori Muller recently began a review of the department's hiring practices M 23 36 2 72 79 She started the review by examining the most critical a growth of the firm, turnover, and the number of"outstanding college seniors ea-financial trainees The firm hires between 60 and 130 financial trainees per year depending on the prospects that it encounters. Virtually all the financial trainees are recruited firom graduating F 21 362 6 B0 Ms. Muller randomly selected 64 files from the 117 candidates who had been hired two years ago and were still on the job. Each file contained the g information (the data are in the accompanying appendix): Traires Number 1. Sex 2. Age whan hired 3. College grade pcin! average 4. "Qualily" of the college attended-ranked from 1 (excellert). M 22 29 1 78 6 18 F 22 35 5 93 09 5, Company index-score an a test devised for the firm. The consultants that cesigned the tastate that it "Vil, rank-order individuals but it probably i nal accurate in assessing the magnitude of the differences between irdivicuals." The test pro- duces a score ranging trom(very unlikely to succeed et the job, to 100 [very likely F 21.03 88 0 to succeed at the jab). s. Second yar perormance evaluation. This evaluatian produces a numerical score fram D (very pccr) to 100 (excelient). Both Muiler and Kochler are certain that the scale is interval in nature. They have also, hased on three years' expenonce with the scale, decided that a score of less than 5D is unsatisfactory·SO-69 is satisfactory 70-69 is above sverage, anc above 89 is excellent. Ms. Mullerhas called you into heroffice and made the foilowing staterment "I'm glad we have a statistician to help us. We're not yet ready to develop a full-blown statistical model of what makes a good recruit. However, it is time to start evaluating some of the variables we have information on. The large number of people we recnuit, the high cost of training them, and the fact that we can't really assess performance until the end of the second year mean that any improvement in our recruiting effectiveness will result in substantial savings for Wells and Assaciates. Would you prepare answers for the following questions 23 2885 71 F 22 2.7 2 8 B5 85 F 23 32 D F 22 52 5 50 F 23 2. 3 5 49 F 22 2.52 30 90 94 for mè M 22 30 1 BS 75 1. Would you summarize the dela so that I can get a feel fer it? 2 Do a higher percertage of males obsain a perlormance score above 69 than d 103 F 23 300 9 females? 3. Do lemales soare higher on the perfarmance evaluation than do males? 4 1$ eree a difference in the performance scores obiained by graduates from tne 107 M 23 3.1 67 57 arious calegcries of colleges? 5. What is the relationship batween grade po n average and parformance score? 6. Whet is the relationship between age when hired and performarce scorG 7, what is tha relationship batween the company index score and Uhe pertormance B Is the petormance evaluaticn raling (excellent, abovs average, etc) Independent I the ca:egory of school atlended? of the sex cf the trainee? grade pairt average Describe the procedure you would use io develop an answer to oach of these . Is the performance evaluation rating (excellent, abova average, eta) indapandent 10How accurately ca we predict performance scores using both age and college queslions. Juslify your approach. b Utilizing the material in the appendix, anwer each questionExplanation / Answer
a)
Descriptive Statistics
N
Minimum
Maximum
Mean
Std. Deviation
Sex
64
.00
1.00
.4844
.50371
Age
64
21.00
35.00
22.8437
2.32460
Colg_grad
64
2.10
3.70
2.7734
.39651
Quality
64
1.00
3.00
1.9375
.77408
CompanyIndex
64
40.00
97.00
73.5625
15.44255
Perfomnace_Eva
64
30.00
99.00
67.7969
17.75064
Valid N (listwise)
64
b)
Sex * Performance Crosstabulation
Performance
Total
1.00
2.00
3.00
4.00
Sex
.00
Count
7
11
8
7
33
% within Sex
21.2%
33.3%
24.2%
21.2%
100.0%
% within Performance
58.3%
47.8%
44.4%
63.6%
51.6%
% of Total
10.9%
17.2%
12.5%
10.9%
51.6%
1.00
Count
5
12
10
4
31
% within Sex
16.1%
38.7%
32.3%
12.9%
100.0%
% within Performance
41.7%
52.2%
55.6%
36.4%
48.4%
% of Total
7.8%
18.8%
15.6%
6.3%
48.4%
Total
Count
12
23
18
11
64
% within Sex
18.8%
35.9%
28.1%
17.2%
100.0%
% within Performance
100.0%
100.0%
100.0%
100.0%
100.0%
% of Total
18.8%
35.9%
28.1%
17.2%
100.0%
here 0 is Female and 1 is male, From this, we can say females obtain a performance score above 89 than males
3)Yes, females score higher on the performance evaluation than male
5) Colage grade point=2.162+.009Performance evaluation
Coefficientsa
Model
Unstandardized Coefficients
Standardized Coefficients
t
Sig.
B
Std. Error
Beta
1
(Constant)
2.162
.182
11.892
.000
Perfomnace_Eva
.009
.003
.404
3.476
.001
a. Dependent Variable: Colg_grad
6) Age=21.734+.016Performance evaluation
Coefficientsa
Model
Unstandardized Coefficients
Standardized Coefficients
t
Sig.
B
Std. Error
Beta
1
(Constant)
21.734
1.156
18.803
.000
Perfomnace_Eva
.016
.017
.125
.992
.325
a. Dependent Variable: Age
7)
Company Index=19.342+.800Performance evaluation
Coefficientsa
Model
Unstandardized Coefficients
Standardized Coefficients
t
Sig.
B
Std. Error
Beta
1
(Constant)
19.342
3.046
6.350
.000
Perfomnace_Eva
.800
.043
.919
18.390
.000
a. Dependent Variable: CompanyIndex
8) We can see here that test statistic is 2.238, p = .897. This tells us that there is no statistically significant association between performance evaluation and quality.
Chi-Square Tests
Value
df
Asymp. Sig. (2-sided)
Pearson Chi-Square
2.238a
6
.897
Likelihood Ratio
2.144
6
.906
Linear-by-Linear Association
1.421
1
.233
N of Valid Cases
64
a. 7 cells (58.3%) have expected count less than 5. The minimum expected count is 2.92.
9) We can see here that test statistic is 1.356, p = .716. This tells us that there is no statistically significant association between performance evaluation and sex
Chi-Square Tests
Value
df
Asymp. Sig. (2-sided)
Pearson Chi-Square
1.356a
3
.716
Likelihood Ratio
1.367
3
.713
Linear-by-Linear Association
.020
1
.887
N of Valid Cases
64
a. 0 cells (.0%) have expected count less than 5. The minimum expected count is 5.33.
10)Here R2 is .165.This model is not perfectly fit
Model Summary
Model
R
R Square
Adjusted R Square
Std. Error of the Estimate
dimension0
1
.406a
.165
.137
16.48882
a. Predictors: (Constant), Age, Colg_grad
Descriptive Statistics
N
Minimum
Maximum
Mean
Std. Deviation
Sex
64
.00
1.00
.4844
.50371
Age
64
21.00
35.00
22.8437
2.32460
Colg_grad
64
2.10
3.70
2.7734
.39651
Quality
64
1.00
3.00
1.9375
.77408
CompanyIndex
64
40.00
97.00
73.5625
15.44255
Perfomnace_Eva
64
30.00
99.00
67.7969
17.75064
Valid N (listwise)
64
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