Statistical Decision Making

This document discusses statistical decision making in the context of Torema Engineering, a company that manufactures transformers. It covers the analysis, tools, and methods used to make statistical decisions, including regression analysis, correlation, and forecasting. The document also explores the problem of managing sales and provides strategies for addressing it. The analysis concludes with the estimation of demand and the importance of accurate data in improving inventory management.

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Running head: Statistical decision making
Statistical decision making
First name Last name
Institution

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Statistical decision making
EXCECUTIVE SUMMARY
The result results from ANOVA output showed that the value of p value at 1.62E-32 was lower
when compared to the assumed level of significance level of 1%. This would help and conclude
that the mean of the sales of transformers in yearly basis would differ from each other. The
conclusion would mean that the sales of transformers and its demand would be fluctuating on
annual basis.
The slope of the regression equation determined was equal to 5.2 this implied that for every unit
increment of the sale of transformers the demand would be expected to increase by 0.811units.
The coefficient of the slope determined is statistically significant this would imply that the linear
relationship of the sample data variable would be significant. The determined coefficient at 0.811
would be regarded as high; this shows that 81.1% variation of the demand of transformer could
be estimated by the sales value of the transformers. Therefore, the regression model showed a
good fit.
The analysis would help to estimate the demand which can minimize the current issues of
overstocking and under stocking. This in long run would maximize the profits and manage
appropriately the company transformers inventory.

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Statistical decision making
TABLE OF CONTENTS
EXCECUTIVE SUMMARY.......................................................................................................................2
INTRODUCTION.......................................................................................................................................4
STATISTICAL ANALYSIS.......................................................................................................................5
INTRODUCTION TO BUSINESS PROBLEM..........................................................................................5
Analysis Plan...........................................................................................................................................6
Quantifiable Factors................................................................................................................................6
PROBLEM STATEMENT..........................................................................................................................7
STATISTICAL TOOLS AND METHODS.................................................................................................8
DATA ANALYSIS AND CONCLUSION...............................................................................................10
GENERAL CONCLUSION......................................................................................................................13
IMPLICATIONS.......................................................................................................................................13
REFERENCES..........................................................................................................................................14

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Statistical decision making
INTRODUCTION
Torema Engineering business is an established business that deals with production and design of
transformers. Torema Australia Pty Ltd was started in 1989 with sole purpose of manufacturing
transformers. Torema business extended its offshore facilities of manufacturing in 2008 with
dedication of manufacturing more transformers. The company expanded drastically and started
manufacturing all types of transformers. Its growth opened other opportunities of expanding its
sub – assemblies to complete assemblies that incorporated other engineering areas. Currently
they are able connect all components together to their own clients rather than just manufacturing
alone. With its 23 years working experience in manufacturing and designing of toroidal type of
transformer products it has helped the company retain strong standing relationship with its
multinational and domestic clients.
Torema Engineering provide design services of its products by accommodating all its
manufacturing and delivering the large number of its orders in time. Its approach is manifested in
all facades of the company, from quality design and ensuring that it delivers its order on time. Its
outstanding relationship has been evident with both authorities of China and Australia. They can
therefore be consulted regarding the standards of transformers products. This is a clear indication
that the manufactured products it produces would comply with all current electrical safety
standards for various appliances.
The head office of Toremo Engineering Company is situated on the northern side of Brisbane.

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Statistical decision making
STATISTICAL ANALYSIS
Torema Engineering business indulges on strong statistical process in order to attain a quality
manufacturing as well as quality control of the transformers it manufactures. The company uses
statistical methods to produce the rightly needed transformers in a position that enables it meet
its demand. The investigative approach applied considers the sales in million dollars made for
the close of 31st December 2018 financial year. The company operation head manager Mr Josie
oversees operation stock. The overstocking and under stocking solutions would be prepared by
the head of process. The sales department focuses on the transformer sales. The core reason for
this analysis would be to identify the total number of transformers which should be manufactured
by the company to intense its production process and sales that company would make.
INTRODUCTION TO BUSINESS PROBLEM
Torema Engineering Company controls its process and ensures quality of its transformer
products. The company primary focuses on manufacturing a balance number of transformers and
refrigerators. The secondary role of Torema Engineering Company is to ensure it maintains a
high quality of transformer products and monitor its production processes. The problem observed
on this case is aligned to the ability of the business company to manage its sales. The company
experiences a challenging task of controlling it sales. The sales value keeps on changing in
certain occasions at particular instances the manufactured products would be more than the
demand while in other occasions the quantity of the transformers manufactured would be less
than supply. To solve the issue, the operation department collected data for 90 variables that
included the sales in million dollars, which would help in identifying the average number of
transformer sales. This would help the company in solving the problem. The main investors in
this case would be the employees who work in the department of operations. The sales team

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Statistical decision making
would be classified as external stakeholders. Both the external stakeholders and internal
stakeholders would play a core role in offering appropriate solution to any company problem.
Analysis Plan
The analysis outlines the directives that would guide in decision making, by first, collecting sales
data. The sales data were collected for 90 variable instances. The information would provide
significant information that would help in solving the stipulated problem. The second step
would be to prepare graphs that would shows increasing and decreasing number of transformer
sales. The fluctuations of sales of transformers would be measured for 90 difference instances.
The third step would be to prepare sales charts in a form of graphs. The department stakeholders
would be concerned with analysing the data and calculating the mean and number of
transformers that would be required to produce the demand. The team would focus on the whole
data results gathered on the stated year.
The generated mean from the 90 sales was accepted to the produce number of transformers. The
operation manager would be expected to pay a core role of motivating employees to work harder
and derive all their efforts to the company in order to make it achieve its demand (Gilbert,
Kogan, Lochstoer and Ozyildirim, 2012). The stated recommendation would be expected to be
adopted by all the stakeholders to ease the proposed implementation.
Quantifiable Factors
The main factor that would automatically affect the internal employees’ performance would
always be laziness. Where the laziness factor would affects the capability of the company getting
the real data. To ensure the laziness is countered then the company would be expected to create
trusty working and healthy environment for its entire employee. The second quantifiable factor
that would affect employees’ performance would be absence of database system of management.

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Statistical decision making
A working system of database management would help on retrieve any kind of data with ease.
Similarly database system would successful provide a timely data that would be appropriate to
provide correct decisions.
PROBLEM STATEMENT
The process of decision making always would be problematic due to fact that there would be a
contradiction to each other. The input provided by each employee should be valued and
appreciated by the employees to help the company overcome any uncertain challenges that might
face the company. The appreciation would contribute to employees being motivated and this
would be gauged as an efficient method of providing solution to problematic question at ease.
Decision making should not only be based on opinions from only two or three stakeholders. The
appropriate method would involve; first, making a committee that comprise of about ten
members and each group or members assigning them either individual or group task. The
committee members would be able to collect and gather information from different avenues to
help solve the problem. The report that would be developed would be sent to the respective
implementation heads who would take appropriate decisions. All employees would then be
expected to abide to the stated decisions that would have to be fully implemented. The process of
abiding to the implemented decision from respective heads would help in solving problematic
question. The heads would ensure that decision suggested would focus on achieving the core
objectives and goals of the company.

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Statistical decision making
Proposing a strategy to address the problem
The strategy proposed would involve adjusting the operation starting from the low ranked staff to
a higher ranked staff. It would be compulsory for each employee to ensure he or she provides
correct, accurate and credible data of supply, manufacture and services to concern department or
team. To curb incompetency then employee who would be found to be providing incorrect data
would be penalised by imposing a hefty penalties this would help stop them from participating in
such kind of practices. The strategies would ensure that the company gets the correct data and
afterward facilitates accurate actual mean calculations. The company would evaluate the
transformer data of sales trends appropriately using graphs. Evaluating the trends of the data of
sales for a particular duration of time would enable the company from using unnecessary and
inaccurate data since the company would be in a position of observing consistency. The
company would also be expected to conduct consistent assessment and data audit. Auditing and
assessment would enable the company to possibly identify inaccuracies and be able to correct
them immediately before they advance and result to wrong decision making by the relevant
company heads. The data that would be gathered inaccurately would result to erroneous mean
calculation and definitely this would result to inaccurate or false conclusion. Therefore, it would
be right to state that accurate results would lead to correct decision making, and this would solve
the company problems (Gilbert, Kogan, Lochstoer and Ozyildirim, 2012).
.
STATISTICAL TOOLS AND METHODS
The appropriate statistical tool that would appropriate to be used for this analysis would be
inferential statistics. This type of statistics normally would be used when the set objectives

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Statistical decision making
would be to test various population claims based on the data provided. The applied tool would be
based on the set objective and the sample distribution. Although, there would be certain use of
descriptive statistics that would help in the estimation of the relationship between variables. It is
important to note that when one use descriptive statistics he or she would tend to summarize the
sample data given or provided (Eriksson & Kovalainen, 2015).
The sample data provided in this particular scenario is numerically in nature. Based on
quantitative variables, the use of descriptive techniques like regression and correlation will be
important. In addition, the hypothetical test would also be performed based on the mean and
standard deviation that pertains the sales.
The appropriate descriptive statistical tool that would be used would include regression analysis,
correlation and forecasting. In regards to statistical inferential, hypothetical test would be the
correct tool of choice. The hypothetical test would be used to estimate the transformers demand.
Also it would be used to determine linear regression significance on the sales of transformers
required. The transformer forecast determines future demand and would be used on regression
account for future transformers estimation sales.
The analysis of time series of the transformer would be performed to determine the trend in
addition to seasonal components (Flick, 2015).
Forecasting together with regression would be used to ensure that estimates of transformer data
would be data driven rather than making random guesses. This is projected to ensure that there
would be reduction on overstocking or under stocking and this would improve inventory
management.

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Statistical decision making
DATA ANALYSIS AND CONCLUSION
The demand of transformer would require three steps, first step, would be to ensure that the
transformers would be unchanged or changed recently. The second step would be to determine
linear relation that exists on the sales of transformer. The time series would be applied when
estimating forecasts on future sales of transformer.
The above statistical method would be regarded as imperative since the hypothetical testing
would assist one to understand if the mean demand of transformers would have changed in
current year or not. In addition the estimation of linear relationship would provide a clear
approximation on the demand of transformer in future. The time series would account for
seasonal changes of the sales of the transformer for annual trends.
The results given would be taken as dependable when we consider the realistic estimation of the
sales and demand of the transformers would be supported using various data and analysis. For
example, the analysis of time series and hypothetical testing would both estimate mean annual
demand of transformer during end of financial year. In addition, the aspect of season has been
catered too when analysing time series.
If we consider the variation in the sales and demand of the transformer, the analysis of ANOVA
would be performed using the variable sales of the transformer.
The result results are shown on figure 1. The value of p value at 1.62E-32 was lower when
compared to the assumed level of significance level of 1%. This would help to conclude that the
mean of the sales of transformers in yearly basis would differ from each other (Fehr and
Grossman, 2013). The conclusion would mean that the sales of transformers and its demand
would be fluctuating on annual basis.

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Statistical decision making
Anova: Single Factor

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Statistical decision making
SUMMARY
Groups Count Sum
Averag
e
Varian
ce
13 88
584.
1 6.6375
17.455
47
1 88 163
1.8522
73
0.5181
56
1 88 210
2.3863
64
0.5156
74
ANOVA
Source of
Variation SS df MS F
P-
value F crit
Between
Groups
1210.1
71 2
605.08
53
98.178
7
1.62E
-32
3.0303
82
Within
Groups
1608.5
69 261
6.1631
01
Total
2818.7
4 263
Figure 1
The future demand and sales of transformer would be forecast appropriately using time series
analysis. The graph of time series has been shown on figure 2 below. The results show that the
sales of the transformers would have upward trends on annual basis. The observations would be
considered as future estimation for both the sales and demand of the transformers.
Transformer sales/demand = 19.038- 5.2*Sales of the transformers
SUMMARY
OUTPUT
Regression Statistics
Multiple R 0.900797
R Square 0.811435
Adjusted
R Square 0.809267
Standard
Error 1.838001

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Statistical decision making
Observatio
ns 89
ANOVA
df SS MS F
Significan
ce F
Regressio
n 1
1264.74
5
1264.7
45
374.3
79 2.87E-33
Residual 87
293.907
6
3.3782
49
Total 88
1558.65
3
Coefficie
nts
Standar
d Error t Stat
P-
value
Lower
95%
Upper
95%
Lower
95.0%
Upper
95.0%
Intercept 19.03827
0.66632
9
28.571
9
5.52E-
46 17.71387
20.362
68
17.713
87
20.362
68
X
Variable 1 -5.2005
0.26877
6
-
19.348
9
2.87E-
33 -5.73473
-
4.6662
8
-
5.7347
3
-
4.6662
8
Figure 2
The slope of the regression equation determined would be equal to 5.2 this would imply that for
a unit increment of the sale of transformers the demand would be expected to increase by
0.811units. The coefficient of the slope determined is statistically significant this would imply
that the linear relationship of the sample data variable would be significant (Hastie, Tibshirani.
and Friedman, 2014). The determined coefficient at 0.811would be regarded as high, this shows
that 81.1% variation of the demand of transformer could be estimated by the sales value of the
transformers. Therefore, the regression model showed a good fit (Hair, Wolfinbarger, Money,
Samouel and Page, 2015).
The analysis would help to estimate the demand which can minimize the current issues of
overstocking and under stocking. This in long run would maximize the profits and manage
appropriately the company transformers inventory.

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Statistical decision making
GENERAL CONCLUSION
The integrity of statistical data would be appropriate in making the correct decision. Torema
Engineering business provides quality and control organization process. The company core
mandate is to manufacture transformers. The problem it encounters is aligned to its capability to
maintain its sales. The company experiences a challenging task in controlling its sales since the
sales are continuously changing in certain occasions at particular instances the manufactured
products would be more than the demand while in other occasions the quantity of the
transformers manufactured would be less than supply.
IMPLICATIONS
According to specified scenario, it appeared that there would be two main objectives for
operating manager in Torema Engineering. The first objective would be to determine if there is
any significant change in transformers demand. Recommendation to the discussed issue would
be to use a forecast model that would be appropriate to be developed in order to determine future
demand of the transformers required.

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Statistical decision making
REFERENCES
Eriksson, P. & Kovalainen, A. (2015). Quantitative methods in business research (3rded.).
London: Sage Publications.
Fehr, F. H., & Grossman, G. (2013).An introduction to sets, probability and hypothesis testing
(3rded.). Ohio: Heath.
Flick, U. (2015). Introducing research methodology: A beginner's guide to doing a research
project (4thed.). New York: Sage Publications.
Gilbert, T., Kogan, S., Lochstoer, L., & Ozyildirim, A. (2012). Investor inattention and the
market impact of summary statistics. Management Science, 58(2), 336-350.
Hair, J. F., Wolfinbarger, M., Money, A. H., Samouel, P., & Page, M. J. (2015). Essentials of
business research methods (2nded.). New York: Routledge.
Hastie, T., Tibshirani, R. & Friedman, J. (2016). The Elements of Statistical Learning
(4thed.). New York: Springer Publications.