Statistical Analysis for Business Decisions

This assignment delves into the application of statistical analysis within the field of auditing. It examines the use of tools like Z-tests to compare population means and ANOVA to analyze variances across different groups. The document provides a practical understanding of p-values, confidence levels, and their significance in drawing conclusions from data. Case examples involving time taken by accountants for tasks and monthly sales figures for various soft drinks illustrate the application of these statistical concepts.

Statistics

Table of Contents
INTRODUCTION...........................................................................................................................1
TASK ..............................................................................................................................................1
1..............................................................................................................................................1
2. ............................................................................................................................................9
3 ...........................................................................................................................................10
4. ..........................................................................................................................................12
5. ..........................................................................................................................................12
6............................................................................................................................................12
7............................................................................................................................................13
8:...........................................................................................................................................13
9: ..........................................................................................................................................14
10. ........................................................................................................................................14
CONCLUSION..............................................................................................................................16
REFERENCES..............................................................................................................................17

INTRODUCTION
Statistics is the main tool which is used by the business analysts for making the business
objectives essential. Although, there are various statistical tools which can help out to make
effective decisions for gaining the sustianablity. This report is based on the statistics data of the
B/M Company which has used statical data for business and economics. The data analysis and
statistical methodology are an integral part of company and demonstration of the text material.
Intention of each method is demonstrate in an application setting, along with statistical outcomes
rendering insights in order to decisions and solutions for the problems.
TASK
1.
a). Applying descriptive data analysis:
Descriptive analysis exactly what name applies they “elaborate” or summarise raw data
and form it something which is interpretable by the human. They are analytical which elaborates
the past. The past means to any point of time which an event which has occurred, whether this is
one minute ago. Descriptive analytics are important as they permits the firm to learn from the
past behaviours, and knowing how they could affect the future outcomes. Here, B/M company's
Uskudar branch and Osman bey branch are having forecasted earnings which are as follows:
Uskudar branch and Osman bey branch monthly expected sales are used for calculating
discriptive statistics.
expected earnings
Month Uskudar branch Osman bey branch
January 30000 28500
February 30400 28350
March 29000 31500
April 31000 30750
May 31500 32100
1

June 28900 60000
July 29000 63000
Augost 31000 64500
September 29000 36000
October 31000 36000
November 31050 34500
December 34500 28350
January 36000 31500
February 38500 32100
March 37000 34500
April 34990 36000
May 35000 31950
June 35400 63000
July 35300 61500
Augost 37990 67500
September 37000 45000
October 41200 34500
November 42000 31800
December 37000 33000
January 42300 34500
February 41000 36450
March 40020 43500
April 41000 45000
May 40050 42000
2

June 40000 75000
July 41400 76500
Augost 39700 75000
September 40030 52500
October 40050 45000
November 43010 42000
December 42020 44700
January 40080 42000
February 43000 40500
March 42000 41700
April 44000 42000
However, Descriptive Statistics are calculated by Uskudar branch which are as follows:
Descriptive Statistics
N Range Minimum Maximum Mean Std. Deviation Variance
Uskudar
branch 40 15100.00 28900.00 44000.00 36834.7500 4811.29440 23148553.782
Valid N
(listwise) 40
Here, From the above mentioned tool, this can be said that number of number of months
monthly earnings is counted as 40 and the total range of the Uskudar branch is 15100. while
minimum and maximum range is calculated as 28900 and 44000. While on the other hand, this
can be said that the company's Uskudar branch mean is calculated as 36834.75 which simply
refers the average number of the set of monthly earnings of entire 40 months earnings. While on
the other hand, this can simply be said that the Uskudar branch is performing well. Discriptive
analytics are useful as they enables us to learn from past behaviours, and know how they may
affect future outcomes. Standard deviation refers to the measure of dispersion of a set of data
from its mean. This measures an absolute variability of a distribution; more dispersion or
variability, higher is the standard deviation and more would be the magnitude of deviation of the
3

value from their mean. Here the standard deviation is calculated as 4811.29. The mean- variance
is the procedure of weighing risk (against) forecasted return. By seeing at the forecasted return
and variance of an asset, investors attempts to form an effective investment choices- forming the
lower variance for a forecasted return or forming an highest forecasted return for a provided
variance level. Variance factor is calculated as the 23148553.782.
Osman Bey beach earnings in different months are mentioned which shows descriptive statistics
are mentioned under this.
Descriptive Statistics
N Range Minimum Maximum Mean Std. Deviation Variance
Osman Bey
Beach 40 48150.00 28350.00 76500.00 43856.2500 14205.56584 201798100.962
Valid N
(listwise) 40
From the above mentioned descriptive Statistics, there are 40 numbers of monthly
earnings which shows descriptive statistics. Here the range is calculated as the range 48150.
while minimum range and maximum range shows maximum and minimum value of the set of
observation. Minimum and maximum range of Osman Bey branch are used by the company for
maintaining sustainability of the company. Here, the mean is an average number of the set of
variables. Standard deviation is the tool which are used by the company for knowing the risk
which are associated to various months earnings. While, variance factor are used by the company
in order to make certain tools that can be used by the company for making the business decisions
effective and efficient.
Coefficient of Correlation between Uskudar and Osman bey branch are mentioned as under.
Which shows that a correlation coefficient is a statistical measure of degree to which changes to
the value of one variable forecast to the value of another. Under this case, the variables are
positive, coefficient of correlation is 0.134705883 which increases the values of the firm.
Coefficient of Correlation 0.134705883
4

Statistics
Uskudar branch
N Valid 40
Missing 0
Mean 36834.7500
Median 37495.0000
Mode 29000.00a
Percentiles 25 31162.5000
50 37495.0000
75 41000.0000
100 44000.0000
a. Multiple modes exist. The smallest
value is shown
Uskudar branch
Frequency Percent Valid Percent Cumulative
Percent
Valid 28900.00 1 2.5 2.5 2.5
29000.00 3 7.5 7.5 10.0
30000.00 1 2.5 2.5 12.5
30400.00 1 2.5 2.5 15.0
31000.00 3 7.5 7.5 22.5
31050.00 1 2.5 2.5 25.0
31500.00 1 2.5 2.5 27.5
34500.00 1 2.5 2.5 30.0
34990.00 1 2.5 2.5 32.5
35000.00 1 2.5 2.5 35.0
35300.00 1 2.5 2.5 37.5
35400.00 1 2.5 2.5 40.0
36000.00 1 2.5 2.5 42.5
37000.00 3 7.5 7.5 50.0
37990.00 1 2.5 2.5 52.5
38500.00 1 2.5 2.5 55.0
39700.00 1 2.5 2.5 57.5
40000.00 1 2.5 2.5 60.0
5

40020.00 1 2.5 2.5 62.5
40030.00 1 2.5 2.5 65.0
40050.00 2 5.0 5.0 70.0
40080.00 1 2.5 2.5 72.5
41000.00 2 5.0 5.0 77.5
41200.00 1 2.5 2.5 80.0
41400.00 1 2.5 2.5 82.5
42000.00 2 5.0 5.0 87.5
42020.00 1 2.5 2.5 90.0
42300.00 1 2.5 2.5 92.5
43000.00 1 2.5 2.5 95.0
43010.00 1 2.5 2.5 97.5
44000.00 1 2.5 2.5 100.0
Total 40 100.0 100.0
6

From the above mentioned graph and calculation, this is found that the company's
measure of central tendency is calculated. Which have mean, median and mode are : 36834.75,
37495, 29000 respectively. While 25th, 50th, 75th, and 100th percentiles are calculated: 31162.5,
37495, 41000, 44000 which shows the data information. Here, histogram Bimodal shape reflects
two peaks. This shape might reflects that the data have emerged from two diverse systems. If this
kind of efforts occurs, two sources must be categorised separately.
Statistics
Osman bey branch
N Valid 40
Missing 0
Mean 43856.2500
Median 41100.0000
Mode 34500.00a
Percentiles 25 32325.0000
50 41100.0000
75 50625.0000
100 76500.0000
a. Multiple modes exist. The smallest
value is shown
Osman bey branch
Frequency Percent Valid Percent Cumulative
Percent
Valid 28350.00 2 5.0 5.0 5.0
28500.00 1 2.5 2.5 7.5
30750.00 1 2.5 2.5 10.0
31500.00 2 5.0 5.0 15.0
31800.00 1 2.5 2.5 17.5
31950.00 1 2.5 2.5 20.0
32100.00 2 5.0 5.0 25.0
33000.00 1 2.5 2.5 27.5
34500.00 4 10.0 10.0 37.5
36000.00 3 7.5 7.5 45.0
36450.00 1 2.5 2.5 47.5
40500.00 1 2.5 2.5 50.0
41700.00 1 2.5 2.5 52.5
7

42000.00 4 10.0 10.0 62.5
43500.00 1 2.5 2.5 65.0
44700.00 1 2.5 2.5 67.5
45000.00 3 7.5 7.5 75.0
52500.00 1 2.5 2.5 77.5
60000.00 1 2.5 2.5 80.0
61500.00 1 2.5 2.5 82.5
63000.00 2 5.0 5.0 87.5
64500.00 1 2.5 2.5 90.0
67500.00 1 2.5 2.5 92.5
75000.00 2 5.0 5.0 97.5
76500.00 1 2.5 2.5 100.0
Total 40 100.0 100.0
8

From the above mentioned graph and diagram, this has been observed that the company's
Osman bey branch is performing better than the uskudar branch. Hence, there is a chance of
having opening of new store.
2.
A). Applying inferential statistics
One-Sample Statistics
N Mean Std. Deviation Std. Error Mean
VAR00005 100 79.5900 13.53491 1.35349
One-Sample Test
Test Value = 100
t df Sig. (2-tailed) Mean Difference 95% Confidence Interval of the
Difference
Lower Upper
VAR00005 -15.080 99 .000 -20.41000 -23.0956 -17.7244
As per this one-sample test, here, significance difference is showing which refers H1. Because,
this represents .000 significance difference.
B). Applying measuring association between monthly sales and monthly commercial costs
Variables Entered/Removeda
Model Variables
Entered
Variables
Removed
Method
1 VAR00007b . Enter
a. Dependent Variable: VAR00005
b. All requested variables entered.
Model Summary
Model R R Square Adjusted R
Square
Std. Error of the
Estimate
1 .289a .083 .051 11140.09220
a. Predictors: (Constant), VAR00007
9

ANOVAa
Model Sum of Squares df Mean Square F Sig.
1 Regression 315953681.742 1 315953681.742 2.546 .122b
Residual 3474846318.25
8 28 124101654.223
Total 3790800000.00
0 29
a. Dependent Variable: VAR00005
b. Predictors: (Constant), VAR00007
Coefficientsa
Model Unstandardized Coefficients Standardized
Coefficients
t Sig.
B Std. Error Beta
1 (Constant) 20801.869 5409.545 3.845 .001
VAR00007 .003 .002 .289 1.596 .122
a. Dependent Variable: VAR00005
Here, VAR007 is assumed to be the independent factor and VAR005 which is assumed to
be the be the dependent variable. Here, the null hypothesis is that is there is no significant
difference between monthly sales and monthly commercial costs.
C). Advantages and disadvantages of SPSS:
Advantage of SPSS: Data could be conveniently imported from Excel or .csv files.
Disadvantage of SPSS: Imported .csv files might not covers variables in an appropriate
numerical format for SPSS, specifically if these have been exported from other another
application like as Mole.
3
A). researcher would use exploratory method while running qualitative statistical research. As
this is based on the facts and figures.
B).
Variables Entered/Removeda
Model Variables
Entered
Variables
Removed
Method
10

1 VAR00007b . Enter
a. Dependent Variable: VAR00005
b. All requested variables entered.
Model Summary
Model R R Square Adjusted R
Square
Std. Error of the
Estimate
1 .973a .947 .945 2733.18253
a. Predictors: (Constant), VAR00007
ANOVAa
Model Sum of Squares df Mean Square F Sig.
1 Regression 3703873638.12
6 1 3703873638.12
6 495.814 .000b
Residual 209168028.541 28 7470286.734
Total 3913041666.66
7 29
a. Dependent Variable: VAR00005
b. Predictors: (Constant), VAR00007
Coefficientsa
Model Unstandardized Coefficients Standardized
Coefficients
t Sig.
B Std. Error Beta
1 (Constant) 7032.164 1327.213 5.298 .000
VAR00007 .009 .000 .973 22.267 .000
a. Dependent Variable: VAR00005
VAR00007 is monthly training costs and VAR00005 is the monthly sales.
Here, there is a significant difference exist between monthly sales and monthly training costs.
Which is the alternative hypothesis.
11

C).
Confirmatory factor analysis is a statistical tools which is implemented in order to confirm the
factor structure of a set of observation variables. While descriptive analysis assist the company
for making the business in an effective manner.
12

4.
Probablity is exactly 1.25 according to the given data and HR manager wants to hire a
new staff if its probability is more than 0.15. henceforth, Hr manager needs to hire to hire staff as
probability of requirement is more than the required margin.
5.
One-Sample Statistics
N Mean Std. Deviation Std. Error Mean
VAR00011 40 502.8500 6.10401 .96513
One-Sample Test
Test Value = 100
t df Sig. (2-tailed) Mean Difference 95% Confidence Interval of the
Difference
Lower Upper
VAR00011 417.405 39 .000 402.85000 400.8978 404.8022
In this case, there is no significant impact on dependent factors. Henceforth, this is null
hypothesis which simply represented as H0.
6.
From the given question, the condition is taken on 3/10 customer and second event is
based on occurrence of first event. I,e. 0.2. So by applying conditional probability formula, we
can calculate that:
13

P(A) = 0.3
P(B)= 0.2 (BASED ON OCCURRENCE OF P(A)
P(B/A)= P(0.3*0.2)/ 0.3
=0.6/0.3= 50%
7
One-Sample Statistics
N Mean Std. Deviation Std. Error Mean
VAR00012 7 19.0000 5.91608 2.23607
VAR00013 7 21.4286 5.91205 2.23455
VAR00014 7 18.2857 6.65117 2.51391
VAR00015 7 23.4286 4.27618 1.61624
One-Sample Test
Test Value = 100
t df Sig. (2-tailed) Mean Difference 95% Confidence Interval of the
Difference
Lower Upper
VAR00012 -36.224 6 .000 -81.00000 -86.4715 -75.5285
VAR00013 -35.162 6 .000 -78.57143 -84.0392 -73.1037
VAR00014 -32.505 6 .000 -81.71429 -87.8656 -75.5630
VAR00015 -47.376 6 .000 -76.57143 -80.5262 -72.6166
Auditors efficiency does have significant impact on the factor dependent variables. As
this is presumes to be the null hypothesis as all the variables represents .0000 figures.
8:
The P-value of all variables are less than 0.05 which indicate that the distribution of
variance is significantly different from one another. The results are determine that the variance of
all three groups are more equal. As, 0.000 (<0.05). The auditors required to make control of
14

other factors those are associated with the research. This analysis attempts to provide a basic
understanding of statistical significance values of p-values and confidence level.
9:
This is said to be two sample Z-test which is helpful in order to determine if population
means are equal or uneven. There are mainly three possibility of developing hypothesis. A
confidence level for the comparison among two mean specifies a wide range of values within the
mean value. If the confidence level consists of 0 it can be said that there is no significance
difference among the mean of the two population at a given confidence level. The Null
hypothesis always assumes that mean value are equal, while the alternatives can either be one
side or two sided. By the use of this, researchers would be able to determine exact results out of
total mean.
10.
a)
Accountants' required time for journalizing & posting (by minutes):
10 12 14
20
27
16
13 13
36
25
21
14
25
17
32 31
14
17 17
27
0
5
10
15
20
25
30
35
40
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Accountants' required time for journalizing &
posting (by minutes)
b).
Soft Drink Purchaes Monthly sales in Units
Coke Classic 24580
Pepsi 35650
15

Sprite 25878
Diet Coke 32580
Dr. Pepper 18585
18%
26%
19%
24% 13%37%
Monthly sales in Units
Coke Classic
Pepsi
Sprite
Diet Coke
Dr. Pepper
c).
0.4 0.56 0.54 0.55 0.57 0.55 0.58 0.56 0.54 0.59 0.54 5.98
0.5 0.45 0.42 0.53 0.56 0.6 0.56 0.54 0.55 0.56 0.58 5.85
0.55 0.54 0.58 0.54 0.54 0.59 0.55 0.58 0.6 0.55 0.57 6.19
0.58 0.56 0.65 0.56 0.57 0.55 0.56 0.6 0.58 0.57 0.59 6.37
0%
20%
40%
60%
80%
100%
Chart Title
Sales Data Week 1 In million Turkish Lira Sales Data Week 2 In million Turkish Lira
Sales Data Week 3 In million Turkish Lira Sales Data Week 4 In million Turkish Lira
16

9.85
8.56
8.66
8.54
8.45
8.67
8.88
Market share %
2010 2011 2012 2013 2014 2015 2016
CONCLUSION
From the above mentioned report, this can be said that the B/M used various statistical tools for
expanding their operations in an effective manner. Although, this is the most effective tool to
know and intrerprat the data in an effective manner.
17