HI6007 - Statistics for Business Decisions: Comprehensive Report

This assignment solution for HI6007 Statistics for Business Decisions provides a detailed analysis of various statistical concepts applied to business data. It includes a comparison of Australian Food and Fibre exports across different states, frequency and class distribution analysis of weekly sales data, and an examination of the relationship between the rate of inflation and the All-Ordinaries Index in Australia from 1995 to 2015. The solution incorporates descriptive statistics, correlation analysis, and simple linear regression to test the significance of the impact of inflation on the All-Ordinaries Index, concluding with a hypothesis test and interpretation of the regression outcome. This assignment is designed to enhance understanding of statistical principles and their application in making informed business decisions. Desklib provides a range of resources, including past papers and solved assignments, to support students in their academic pursuits.

Running head: STATISTICS FOR BUSINESS DECISIONS
Statistics for Business
Name of the Student:
Name of the University:
Author note:

1STATISTICS FOR BUSINESS DECISIONS
Table of Contents
Answer 1..........................................................................................................................................2
Answer 2..........................................................................................................................................4
Answer 3..........................................................................................................................................6
References......................................................................................................................................12

2STATISTICS FOR BUSINESS DECISIONS
Answer 1
a)
Victoria Queensland NSW WA SA Tasmania Others
0
2,000
4,000
6,000
8,000
10,000
12,000
14,000
7,344
4,872 4,959 4,219 3,391
907 973
11,656
8,179
6,979 6,350
5,255
736
4,278
Australian Food and Fibre exports
($million)
Exports ($million) 2010 Exports ($million) 2015
Figure 1: Australian Food and Fibre Exports ($million)
b)
Victoria Queensland NSW WA SA Tasmania Others
0.00%
5.00%
10.00%
15.00%
20.00%
25.00%
30.00% 27.54%
18.27% 18.60%
15.82%
12.72%
3.40% 3.65%
26.84%
18.83%
16.07% 14.62%
12.10%
1.69%
9.85%
Food and Fibre exports ($million, %)
2010 2015

3STATISTICS FOR BUSINESS DECISIONS
Figure 2: Australian Food and Fibre Exports ($million, %)
c) The Australian Food and Fibre export in $million and in percentage values for the years
2010 and 2015 for each of the states and other regions of Australia have been compared
in the graphs above. Both of the graphs show that Victoria among all the states has
contributed maximum in the total value of exports in $million as well as in percentage
values. It can be seen from the first graph that 2015 experienced a substantial increase in
the total value of exports of food and fibre from all the states than in 2010. The rate of
increase in the export value in $million has been similar and the trend has been consistent
for all the states from 2010 to 2015. Export value is higher for ‘Others’, than for
Tasmania.
The second graph shows the contribution of the Australian states in the food and
fibre exports in terms of percentage of $million for 2010 and 2015. As the total export
value has increased quite significantly in 2015, the proportion of the contribution of the
states has changed too. The percentage contribution of the states were higher in 2010 than
in 2015 except for Queensland.

4STATISTICS FOR BUSINESS DECISIONS
Answer 2
(a) and (b)
Classes Frequency Relative
Frequency
Cumulative
Frequency
Cumulative
Relative
Frequency
0 - 4 4 0.1 4 0.100
5 - 9 9 0.225 13 0.325
10 - 14 7 0.175 20 0.500
15 - 19 11 0.275 31 0.775
20 - 24 2 0.05 33 0.825
25 - 29 5 0.125 38 0.950
30 - 34 2 0.05 40 1.000
Total 40 1 40 1
Table 1: Frequency and class distribution of weekly sales data
d) Relative frequency histogram

5STATISTICS FOR BUSINESS DECISIONS
0 - 4 5 - 9 10 - 14 15 - 19 20 - 24 25 - 29 30 - 34
0
0.05
0.1
0.15
0.2
0.25
0.3
Relative Frequency Histogram
Figure 3: Relative frequency histogram
e) Ogive for the data
0 - 4 5 - 9 10 - 14 15 - 19 20 - 24 25 - 29 30 - 34
0
5
10
15
20
25
30
35
40
45
4
13
20
31 33
38 40
Cumulative Frequency
Figure 4: Ogive
e) Proportion of data less than 20 is:
0.775 (gained from the cumulative relative frequency of data less than 20)

6STATISTICS FOR BUSINESS DECISIONS
f) Proportion of data more than 24 is:
1 – 0.825 = 0.175 (gained from the cumulative relative frequency of data more than 24)

7STATISTICS FOR BUSINESS DECISIONS
Answer 3
a) Rate of inflation (%) trend in Australia, 1995 – 2015
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
1.9
4.6
2.6
0.3
1.3
2.4
5.9
2.9 3.0
2.4 2.4
2.9 2.5
4.3
2.4
2.9 3.3
1.6
2.5 2.9
1.5
Rate of Inflation (%)
Figure 5: Rate of Inflation (%), 1995-2015
All-Ordinaries Index trend in Australia, 1995 – 2015
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
0.0
1000.0
2000.0
3000.0
4000.0
5000.0
6000.0
7000.0
All-Ordinaries index

8STATISTICS FOR BUSINESS DECISIONS
Figure 6: All-Ordinaries Index, 1995-2015
b) Plot depicting the relationship between Rate of Inflation (%) and All-Ordinaries Index
0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0
0.0
1000.0
2000.0
3000.0
4000.0
5000.0
6000.0
7000.0
f(x) = 40.3077051702228 x + 3874.28641228011
R² = 0.00151127464405965
Rate of Inflation (%) and All-Ordinaries index
Figure 7: Relationship between Rate of Inflation (%) and All-Ordinaries
Index
The above scatter plot shows X as the independent variable, that is, Rate of Inflation (%),
and Y as dependent variable, that is, All-Ordinaries Index and their relationship. All-
Ordinaries Index is influenced by the Rate of Inflation (%). These variables are
accordingly represented in the appropriate axes.

9STATISTICS FOR BUSINESS DECISIONS
c) Numerical summary report (Descriptive statistics): Rate of Inflation (%) and All-
Ordinaries Index
Rate of inflation (%) All-Ordinaries index
Mean 2.69 3982.73
Standard Error 0.26 269.99
Median 2.50 4127.60
Mode 2.4 #N/A
Standard Deviation 1.19 1237.25
Sample Variance 1.42 1530783.22
Kurtosis 2.04 -1.01
Skewness 0.80 0.18
Range 5.6 4336.8
Minimum 0.3 2000.8
Maximum 5.9 6337.6
Sum 56.5 83637.4
Count 21 21
1st Quartile 2.4 3032
3rd Quartile 2.9 4933.5
Table 2: Descriptive statistics: Rate of Inflation (%) and All-Ordinaries Index
d) Value of Correlation Coefficient (r) between Rate of Inflation (%) and All-Ordinaries
Index
Rate of inflation (%) All-Ordinaries index
Rate of inflation (%) 1
All-Ordinaries index 0.0389 1
Table 3: Correlation between Rate of Inflation (%) and All-Ordinaries Index

10STATISTICS FOR BUSINESS DECISIONS
The value of correlation coefficient (r) between All-Ordinaries Index and Rate of
Inflation (%) is 0.0389. It is positive. The range of the value of correlation coefficient is
+1 to -1. The closer the value of r to +1, stronger is the positive correlation between the
dependent and independent variables, and closer the value to -1, stronger is the negative
correlation. In case of zero, there is no correlation between the variables. Hence,
correlation coefficient values closer to zero imply insignificant correlation between the
independent and dependent variables (Beyer 2019). Here, the value of the correlation
coefficient between All-Ordinaries Index and Rate of Inflation (%) is 0.0389, which is
positive but much nearer to zero. Thus, it is evident that the variables have positive
correlation although the magnitude of the impact is not much strong.
e) The equation for Simple linear regression model:
Y =mX +C
where, Y is the Dependent variable, that is, All-Ordinaries Index
X is the Independent variable , that is, Rate of Inflation (%)
and, C is Constant.
The hypothesis to be tested is:
H0 (Null hypothesis): Impact of Rate of Inflation (%) on All-Ordinaries Index is not
significant.
H1 (Alternate hypothesis): Impact of Rate of Inflation (%) on All-Ordinaries Index is
significant.
Regression outcome:

11STATISTICS FOR BUSINESS DECISIONS
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.0389
R Square 0.0015
Adjusted R Square -0.0510
Standard Error 1268.4304
Observations 21
ANOVA
df SS MS F
Significance
F
Regression 1 46268.68 46268.68 0.029 0.867
Residual 19 30569395.73 1608915.56
Total 20 30615664.41
Coefficient
s
Standard
Error t Stat P-value
Intercept 3874.29 696.83 5.560 0.000
Rate of inflation (%) 40.31 237.69 0.170 0.867
Table 4: Simple linear regression model
f) R2 (Coefficient of determination) = 0.0015.
Value of R2 (Coefficient of determination) describes the proportion of variance in the
dependent variable, which can be predicted by the independent variable. As stated by
Murphy and Katz (2019), R2 defines how much variations in the dependent variable can
be attributed to the independent variable. It presents the best fit of the dependent variable
to the fitted line of linear regression. Here, R2 value is 0.0015, that is, the independent
variable (Rate of Inflation (%)) can explain only 0.15% of the variation in the dependent
variable (All-Ordinaries Index), which is highly insignificant. The line plot in Figure 6
shows that the observations of the dependent variable are scattered and are not much