MGSC 2207 Saint Marys University Delta Wire Statistics Business Report There are business report, its example from the prof and several tables that helps t

MGSC 2207 Saint Marys University Delta Wire Statistics Business Report There are business report, its example from the prof and several tables that helps to finish the report in the attached file, and a simple 3 bonus question need to be answered1.What is ANOVA?2.What is chi square?3.What is practical significanc BUSINESS REPORT: DELTA WIRE
Marks: Please see the section on Revised Marking Scheme in the new approved course outline
dated 22 March 2020. For those who missed the midterm, see the section entitled Students Who
Missed the Midterm.
Due date: The deadline for electronic submission of this business report is 17 April 2020,
though students are encouraged to submit this report earlier. Students should bear in mind
university policies regarding cheating (see the section on cheating in this course outline).
Method of submission: Ensure that you attach to this business report submission your
answers to the bonus questions (if you choose to try for these extra bonus points = 5%).
Use the Brightspace drop boxes that I will be setting up soon for each class. Ensure that
you submit it to the drop box for the class in which you are registered. Do NOT send your
business report directly to me. I will let you know by e-mail when the drop boxes are created.
Ensure that the subject line of your submission states the name of this problem (Delta Wire)
and gives your full name plus the class you are registered in (state the class days and times for
the class in which you are registered) plus your A number. Example subject line: Delta Wire
Report — John Doe (TTh 10:00am) A00111111.
Problem: Delta Wire manufactures high-carbon specialty steel wire and at present employs
20,000 workers. The company is currently experiencing serious problems, at least in part due to
the continuing decline in value of the CDN$. Foreign competition is becoming a significant
threat to Delta’s market position. At the same time, industry quality requirements have become
increasingly tougher each year. One strength at Delta, however, is their level of employee
education. Employee education has many payoffs, but one, in particular, has been suggested
several times at recent executive meetings. Some managers believe that education has resulted in
a more positive outlook and interest in implementing what has been learned and as a result, the
more education received by a worker, the less likely he/she is to miss workdays (education may
reduce absenteeism). Others, however, insist that the opposite is true (education stifles the free
spirit leading to more absenteeism). The data addressing this issue is displayed in the table below
for a random sample of 20 company employees with the number of hours of company education
received and the number of days of sick leave taken.
Analysis: Use Excel to analyse this data statistically. Ensure that you conduct a correlation and
regression analysis though it is possible other statistical analyses might also be warranted.
Business report: Write a formal business report to your “boss” at the company. The purpose of
this business report is to permit you to show what you have learned in the course about statistics,
in particular what you have learned about correlation and regression, and what should be
included in a practical business report using statistical analyses.
Students must submit a concise business report for which they should:
Utilize appropriate statistical analyses of the sample data provided
Interpret the results in the context of a business situation
Discuss the statistical results in the context of the business situation
Discuss any problems or shortcomings with the way the study was conducted (if any)
If necessary, describe methods of improving the study
Discuss any recommendations you think appropriate
Assume that you are writing this report so that it can be read by two types of readers: those
who know no statistics (such as your “boss” at this company) and those who know statistics
(such as her statistics expert assistant who will want enough information to know if you analysed
the data properly and whether you have drawn the correct conclusions). Use anything you have
learned throughout this course when composing your comprehensive, yet concise, wellorganized and well-written report.
Instructions: The business report is strictly limited to a maximum of 3 pages, 12-point, doublespaced, Times Roman (not including title page, graphs, tables, references, or appendices). Ensure
all Excel analyses are attached. This report should be written in essay-format (i.e., sentences and
paragraphs), not point form.
Criteria for evaluation will include appropriateness and correctness of analyses; quality and
thoroughness of analyses; quality of organization and writing; clarity and correctness of
interpretation; professional quality of job performed.
Data:
Employee
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Hours of
Education
24
16
48
120
36
10
65
36
0
12
8
60
0
28
15
88
120
15
48
5
Sick Days
5
4
0
1
5
7
0
3
12
8
8
1
9
3
1
2
1
8
0
10
WGI – HUMAN RESOURCES: PAY INCREASES REPORTKELSEY B.
Comprised of data from 19 non-salaried work crew members of WGI, this report provides both graphical
and numerical data and represents the current and new pay rates of these workers. This report is aimed
to provide insight on the extra labor costs to be incurred in the sewer line installation project in
Madison, Wisconsin. More specifically, this report focuses on the rate increases of the non-salaried
workers of WGI that will be working on the new sewer line project. First, this report will focus on the
current rates, followed by the new rates and concluded with the pay increases data. All calculations
have been calculated using the data from WGI databases and can be seen in great detail the appendix of
this report.
The
histogram
representing
the
distribution
of
current pay to the
WGI’s non-salaried
workers can be
seen
below.
Looking at this
histogram you can
see that most of
the workers are
paid between $16
and $20 per hour,
with
similar
frequencies among the other pay rates.
The current rate mean is $19.10. This means that of the 19 non-salaried employees, the average
earnings per hour is $19.10.
The median for the current pay rate is $18.36. The median which is the middle number in a set of data
splits the data into equal halves. This means that the center or middle value of the 19 employees is
currently $18.36.
The range which is the difference between the maximum and the minimum value is useful for finding
the level of variation in a set of data. The current rate range is $13.27. This means that there is a $13.27
difference between the highest paid employee and the lowest paid employee.
The current and new rate variance is used to indicate how widely the pay rates of WGI’s employees vary
from one non-salaried employee to the next non-salaried employee in our sample of 19 employees. The
current rate variance is $13.11 and the standard deviation is $3.62. This means that between any two
random individuals their per hour wage would vary by $3.62.
The coefficient of variation is used to measure the variation or difference relative to the mean, which is
also known as the average. The current rate coefficient of variation is equal to 18.98%. We would expect
the two percentages of the current and new rates to be very close because the pay increases were not
extreme, the highest increase being $2.00, therefore the rates compared to other employee rates were
pretty evenly increased.
The histogram shown
below is similar to the
one above however it
represents the new pay
rates of the non-salaried
employees, which is
their current rate plus
their pay increases.
Similar to the current
pay wages, most of the
employees are paid
between $16 and $20
per hour, however with
the new pay increases
employees pay has risen in the $21 to $25 dollar range.
The new rate mean is slightly higher than the current rate mean sitting at $20.06. This means that with
the new pay increases the average earnings per hour of the 19 non-salaried WGI employees by $0.96 to
$20.06.
The new rate median has once again increased with the pay increases. The new pay rate median is
$19.28, which means that $19.28 is the new center or middle value.
The new rate range is lower than that of the current rate range at $12.52 which means that there is less
variation between the amount that each employee gets paid by the hour. Since the new rate range is
lower than that of the current rate range it means that employees are getting paid more equally with
the new pay increases than with the current rate per hour.
The new rate variance equals $13.17 which is close to that of the current rate variance. Since the
variance of the two rates is similar which means that we should expect the standard deviation to be
close too. This is the case, where the new rate standard deviation is $3.63. This means again that if two
people are randomly chosen their wages would vary by $3.63.
The new rate coefficient of variation is 18.09%. These results show that the new rate coefficient of
variation is slightly smaller than that of the current rate variation which means that the new rate varies
slightly less than the current rate, so there is a slightly smaller difference between the employees per
hour wages with the new rate.
This pay increase
histogram displays
the increases from
the pay rates from
the current rate to
the new rates. As
you can see the pay
increases
range
from $0.40 to $2.00
with the highest
number of pay
increases
being
between $0.41 and
$0.80. There are very few pay increases at either extreme and are distributed in the middle three bars of
the histogram.
From this data we can conclude that the mean or average pay increase is $0.97. We can also conclude
that the median or pay increase that is in the middle dividing the data set into two equal parts is $0.85.
The range for this set of data is equal to $1.60, which means that there is $1.60 between the highest pay
increase and the lowest pay increase.
The pay increase variance is $0.19 and the standard deviation for this set of data is $0.44. This once
again means that between two randomly chosen pay increases the difference will be $0.44. The pay
increase coefficient of variation is equal to 44.92% which is much higher than the coefficient of variation
between the current and new rates.
To conclude, the current and new rate means are $19.10 and $20.06. The pay increases range from
$0.40 to $2.00 per hour and are highly distributed in the $0.40 to $0.80 range. The mean and standard
deviation for the pay increases are $0.97 an $0.44 respectively. This data gives you the insight on the
pay increases of the non-salaried employees of WGI. This will allow you to make informed decisions
about the new sewer line project and will help you to determine what these things will mean for future
business.
APPENDIX
Mean = ?X / N
Current Rate Mean = $20.55 + $22.15 + $14.18 +$14.18 + $18.80 + $18.98 + $25.24 + $18.36 + $17.20
+ $16.99 + $16.45 + $18.90 + $18.30 + $27.45 + $16.00 + $17.47 + $23.99 + $22.62 + $15.00
Current Rate Mean = 362.81 / 19
Current Rate Mean = $19.095
New Rate Mean = $22.55 + $23.81 + $15.60 + $15.60 + $20.20 + $20.20 + $26.42 + $19.28 + $18.06 +
$17.84 + $17.27 + $19.66 + $19.02 + $28.12 + $16.64 + $18.00 + $24.47 + $23.08 + $15.40
New Rate Mean = 381.22 / 19
New Rate Mean = $20.06
Pay Increase Mean = 2.00 + 1.66………………+0.40 / 19
Pay Increase Mean= 18.42 /19
Pay Increase Mean= $0.9695
Median (i) = ½(n)
Current Rate Median = ½ (19) = 9.5 ? 10
Current Rate Median = $18.36
New Rate Median = $19.28
Pay Increase Median = $0.85
Range (R) = Maximum Value – Minimum Value
Current Rate Range = $27.45 – $14.18
Current Rate Range= $13.27
New Rate Range = $28.12 – $15.60
New Rate Range= $12.52
Pay Increase Range = $2.00 – $0.40
Pay Increase Range= $1.60
Population Variance: O2 = ?x^2 – (?x)^2/ N / N
Current Rate Variance: X=362.81 & X^2= 7176.9879
= 7176.9879 – (362.81)^2/19 /19
= 7176.9879 – 131631.0961/19 /19
= 7176.9879 – 6927.952426 / 19
= 249.035174 / 19
Current Rate Variance= $13.1071
Standard Deviation = ?13.1071
Current Rate Standard Deviation= $3.6204
New Rate Variance: x=381.22 & X^2= 7899.1628
= 7899.1628 – (381.22)^2 / 19 /19
= 7899.1628 – 145328.6884/19 /19
= 7899.1628 – 7648.878337 /19
= 250.284463 /19
New Rate Variance= $13.1729
Standard Deviation = ?13.1729
New Rate Standard Deviation= $3.6294
Pay Increase Variance: X= 18.42 & X^2= 21.461
= 21.461 – (18.42)^2/19 /19
= 21.461 – (339.2964/19) /19
= 21.461 – 17.85770526 /19
= 3.60329/19
Pay Increase Variance= 0.189647091
Standard Deviation = ?0.189647091
Pay Increase Standard Deviation= $0.435484892
Sample Coefficient of Variation (CV) = s/
(100)%
Current Rate Coefficient of Variation = 3.6204 / 19.095 (100)%
Current Rate Coefficient of Variation= 18.96%
New Rate Coefficient of Variation = 3.6294 / 20.06 (100)%
New Rate Coefficient of Variation= 18.09%
Pay Increase Coefficient of Variation = 0.432484892/0.9695(100)%
Pay Increase Coefficient of Variation= 44.9185%
Pay Increases:
Jody – $2.00
Tim – $1.66
Thomas – $1.42
Shari – $1.42
John – $1.40
Jared – $1.22
Loren – $1.18
Mike – $0.92
Patrick –$0.86
Sharon – $0.85
Sam – $0.82
Susan – $0.76
Chris – $0.72
Steve F – $0.68
Kevin – $0.64
Larry – $0.53
Mary Ann – $0.48
Mark – $0.46
Aaron – $0.40
Standard Normal Distribution
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.0
0.0000
0.0040
0.0080
0.0120
0.0160
0.0199
0.0239
0.0279
0.0319
0.0359
0.1
0.0398
0.0438
0.0478
0.0517
0.0557
0.0596
0.0636
0.0675
0.0714
0.0753
0.2
0.0793
0.0832
0.0871
0.0910
0.0948
0.0987
0.1026
0.1064
0.1103
0.1141
0.3
0.1179
0.1217
0.1255
0.1293
0.1331
0.1368
0.1406
0.1443
0.1480
0.1517
0.4
0.1554
0.1591
0.1628
0.1664
0.1700
0.1736
0.1772
0.1808
0.1844
0.1879
0.5
0.1915
0.1950
0.1985
0.2019
0.2054
0.2088
0.2123
0.2157
0.2190
0.2224
0.6
0.2257
0.2291
0.2324
0.2357
0.2389
0.2422
0.2454
0.2486
0.2517
0.2549
0.7
0.2580
0.2611
0.2642
0.2673
0.2704
0.2734
0.2764
0.2794
0.2823
0.2852
0.8
0.2881
0.2910
0.2939
0.2967
0.2995
0.3023
0.3051
0.3078
0.3106
0.3133
0.9
0.3159
0.3186
0.3212
0.3238
0.3264
0.3289
0.3315
0.3340
0.3365
0.3389
1.0
0.3413
0.3438
0.3461
0.3485
0.3508
0.3531
0.3554
0.3577
0.3599
0.3621
1.1
0.3643
0.3665
0.3686
0.3708
0.3729
0.3749
0.3770
0.3790
0.3810
0.3830
1.2
0.3849
0.3869
0.3888
0.3907
0.3925
0.3944
0.3962
0.3980
0.3997
0.4015
1.3
0.4032
0.4049
0.4066
0.4082
0.4099
0.4115
0.4131
0.4147
0.4162
0.4177
1.4
0.4192
0.4207
0.4222
0.4236
0.4251
0.4265
0.4279
0.4292
0.4306
0.4319
1.5
0.4332
0.4345
0.4357
0.4370
0.4382
0.4394
0.4406
0.4418
0.4429
0.4441
1.6
0.4452
0.4463
0.4474
0.4484
0.4495
0.4505
0.4515
0.4525
0.4535
0.4545
1.7
0.4554
0.4564
0.4573
0.4582
0.4591
0.4599
0.4608
0.4616
0.4625
0.4633
1.8
0.4641
0.4649
0.4656
0.4664
0.4671
0.4678
0.4686
0.4693
0.4699
0.4706
1.9
0.4713
0.4719
0.4726
0.4732
0.4738
0.4744
0.4750
0.4756
0.4761
0.4767
2.0
0.4772
0.4778
0.4783
0.4788
0.4793
0.4798
0.4803
0.4808
0.4812
0.4817
2.1
0.4821
0.4826
0.4830
0.4834
0.4838
0.4842
0.4846
0.4850
0.4854
0.4857
2.2
0.4861
0.4864
0.4868
0.4871
0.4875
0.4878
0.4881
0.4884
0.4887
0.4890
2.3
0.4893
0.4896
0.4898
0.4901
0.4904
0.4906
0.4909
0.4911
0.4913
0.4916
2.4
0.4918
0.4920
0.4922
0.4925
0.4927
0.4929
0.4931
0.4932
0.4934
0.4936
2.5
0.4938
0.4940
0.4941
0.4943
0.4945
0.4946
0.4948
0.4949
0.4951
0.4952
2.6
0.4953
0.4955
0.4956
0.4957
0.4959
0.4960
0.4961
0.4962
0.4963
0.4964
2.7
0.4965
0.4966
0.4967
0.4968
0.4969
0.4970
0.4971
0.4972
0.4973
0.4974
2.8
0.4974
0.4975
0.4976
0.4977
0.4977
0.4978
0.4979
0.4979
0.4980
0.4981
2.9
0.4981
0.4982
0.4982
0.4983
0.4984
0.4984
0.4985
0.4985
0.4986
0.4986
3.0
0.4987
0.4987
0.4987
0.4988
0.4988
0.4989
0.4989
0.4989
0.4990
0.4990
t distribution
One-tail ?
two-tail ?
df
0.4
0.8
0.25
0.5
0.1
0.2
1.00
0.325
1.000
3.078
6.314
12.706
2.00
0.289
0.816
1.886
2.920
3.00
0.277
0.765
1.638
2.353
4.00
0.271
0.741
1.533
5.00
0.267
0.727
6.00
0.265
7.00
0.005
0.01
0.001
0.002
0.0005
0.001
31.821
63.657
318.310
636.619
4.303
6.965
9.925
22.326
31.599
3.182
4.541
5.841
10.213
12.924
2.132
2.776
3.747
4.604
7.173
8.610
1.476
2.015
2.571
3.365
4.032
5.893
6.869
0.718
1.440
1.943
2.447
3.143
3.707
5.208
5.959
0.263
0.711
1.415
1.895
2.365
2.998
3.499
4.785
5.408
8.00
0.262
0.706
1.397
1.860
2.306
2.896
3.355
4.501
5.041
9.00
0.261
0.703
1.383
1.833
2.262
2.821
3.250
4.297
4.781
10.00
0.260
0.700
1.372
1.812
2.228
2.764
3.169
4.144
4.587
11.00
0.260
0.697
1.363
1.796
2.201
2.718
3.106
4.025
4.437
12.00
0.259
0.695
1.356
1.782
2.179
2.681
3.055
3.930
4.318
13.00
0.259
0.694
1.350
1.771
2.160
2.650
3.012
3.852
4.221
14.00
0.258
0.692
1.345
1.761
2.145
2.624
2.977
3.787
4.141
15.00
0.258
0.691
1.341
1.753
2.131
2.602
2.947
3.733
4.073
16.00
0.258
0.690
1.337
1.746
2.120
2.583
2.921
3.686
4.015
17.00
0.257
0.689
1.333
1.740
2.110
2.567
2.898
3.646
3.965
18.00
0.257
0.688
1.330
1.734
2.101
2.552
2.878
3.610
3.922
19.00
0.257
0.688
1.328
1.729
2.093
2.539
2.861
3.579
3.883
20.00
0.257
0.687
1.325
1.725
2.086
2.528
2.845
3.552
3.850
21.00
0.257
0.686
1.323
1.721
2.080
2.518
2.831
3.527
3.819
22.00
0.256
0.686
1.321
1.717
2.074
2.508
2.819
3.505
3.792
23.00
0.256
0.685
1.319
1.714
2.069
2.500
2.807
3.485
3.768
24.00
0.256
0.685
1.318
1.711
2.064
2.492
2.797
3.467
3.745
25.00
0.256
0.684
1.316
1.708
2.060
2.485
2.787
3.450
3.725
26.00
0.256
0.684
1.315
1.706
2.056
2.479
2.779
3.435
3.707
27.00
0.256
0.684
1.314
1.703
2.052
2.473
2.771
3.421
3.690
28.00
0.256
0.683
1.313
1.701
2.048
2.467
2.763
3.408
3.674
29.00
0.256
0.683
1.311
1.699
2.045
2.462
2.756
3.396
3.659
30.00
0.256
0.683
1.310
1.697
2.042
2.457
2.750
3.385
3.646
40.00
0.681
1.303
1.684
2.021
2.423
2.704
3.307
3.551
50.00
0.679
1.299
1.676
2.009
2.403
2.678
3.261
3.496
60.00
0.679
1.296
1.671
2.000
2.390
2.660
3.232
3.460
90.00
0.677
1.291
1.662
1.987
2.369
2.632
3.185
3.403
1.289
1.658
1.980
2.358
2.617
3.160
3.373
1.282
1.645
1.960
2.326
2.576
3.090
3.291
120.00
inf
0.253
0.674
0.05
0.025
0.01
0.1
0.05
0.02
Critical values ofstudent’s t
F Distribution
Degrees of freedom – numerator
df
den
Area in
upper
tail
1
0.10
39.863
49.500
53.593
55.833
57.240
58.204
58.906
59.439
59.858
0.05
161.448
199.500
215.707
224.583
230.162
233.986
236.768
238.883
240.543
0.025
647.789
799.500
864.163
899.583
921.848
937.111
948.217
956.656
963.285
0.01
4052.18
4999.50
5403.35
5624.58
5763.65
5858.99
5928.36
5981.07
6022.47
2
3
4
5
6
7
8
9
10
11
1
2
3
4
5
6
7
8
9
0.10
8.526
9.000
9.162
9.243
9.293
9.326
9.349
9.367
9.381
0.05
18.513
19.000
19.164
19.247
19.296
19.330
19.353
19.371
19.385
0.025
38.506
39.000
39.166
39.248
39.298
39.332
39.355
39.373
39.387
0.01
98.503
99.000
99.166
99.249
99.299
99.333
99.356
99.374
99.388
0.10
5.538
5.462
5.391
5.343
5.309
5.285
5.266
5.252
5.240
0.05
10.128
9.552
9.277
9.117
9.014
8.941
8.887
8.845
8.812
0.025
17.443
16.044
15.439
15.101
14.885
14.735
14.624
14.540
14.473
0.01
34.116
30.817
29.457
28.710
28.237
27.911
27.672
27.489
27.345
0.10
4.545
4.325
4.191
4.107
4.051
4.010
3.979
3.955
3.936
0.05
7.709
6.944
6.591
6.388
6.256
6.163
6.094
6.041
5.999
0.025
12.218
10.649
9.979
9.605
9.365
9.197
9.074
8.980
8.905
0.01
21.198
18.000
16.694
15.977
15.522
15.207
14.976
14.799
14.659
0.10
4.060
3.780
3.619
3.520
3.453
3.405
3.368
3.339
3.316
0.05
6.608
5.786
5.410
5.192
5.050…
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