HI6007: Statistics for Business Decisions Group Assignment T3 2019

This assignment solution addresses statistical concepts relevant to business decision-making. It includes an analysis of food and fiber export data, exploring trends and percentages. The solution also covers descriptive statistics, such as frequency distributions, histograms, and ogives, using a dataset ...Read More

Running head: STATISTICS FOR BUSINESS DECISIONS
Statistics for Business Decisions
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2Statistics for business decisions
Table of Contents
Solution 1...................................................................................................................................4
Answer to the question (a).....................................................................................................4
Figure 1: Food and Fibre Export 2010...................................................................................4
Figure 2: Food and Fibre Export 2015...................................................................................4
Answer to the question (b).....................................................................................................5
Figure 3: Percentage of Food and Fibre Export 2010............................................................5
Figure 4: Percentage of Food and Fibre Export 2015............................................................5
Answer to the question (c).....................................................................................................6
Solution 2...................................................................................................................................6
Answer to the question 2 (c)..................................................................................................6
Figure 5: Histogram on Relative Frequency..........................................................................6
Answer to the question 2 (d)..................................................................................................7
Figure 6: Ogive on weekly Sales...........................................................................................7
Answer to the question (e).....................................................................................................7
Answer to the question (f)......................................................................................................7
Solution 3...................................................................................................................................8
Answer to the question (a).....................................................................................................8
Figure 7: Trend line of Rate of Inflation (%).........................................................................8
Figure 8: Trend line of all - ordinaries index.........................................................................8
Answer to the question (b).....................................................................................................9
Figure 9: Scatter plot..............................................................................................................9

3Statistics for business decisions
Answer to the question (c)...................................................................................................10
Answer to the question (d)...................................................................................................11
Answer to the question (e)...................................................................................................11
Answer to the question (f)....................................................................................................11
Answer to the question (g)...................................................................................................11
Answer to the question (g)...................................................................................................12
References................................................................................................................................13

4Statistics for business decisions
Solution 1
Answer to the question (a)
Victoria
Queensland
NSW
WA
SA
Tasmania
Others
0 1000 2000 3000 4000 5000 6000 7000 8000
7344
4872
4959
4219
3391
907
973
Food and Fibre Export 2010
Frequency
State
Figure 1: Food and Fibre Export 2010
Victoria
Queensland
NSW
WA
SA
Tasmania
Others
0 2,000 4,000 6,000 8,000 10,000 12,000
11,656
8,179
6,979
6,350
5,255
736
4,278
Food and Fibre Export 2015
Frequency
State
Figure 2: Food and Fibre Export 2015

5Statistics for business decisions
Answer to the question (b)
Victoria
Queensland
NSW
WA
SA
Tasmania
Others
0 5 10 15 20 25 30
27.5417213575848
18.2711419463717
18.5974123382711
15.8222388899306
12.717044815301
3.40146259141196
3.64897806112882
Percentage of Food and Fibre Export
on 2010
Frequency
State
Figure 3: Percentage of Food and Fibre Export 2010
Victoria
Queensland
NSW
WA
SA
Tasmania
Others
0 5 10 15 20 25 30
26.836737043262
18.8313033868257
16.0684272327493
14.6202196486543
12.0990951580595
1.69456404116685
9.84965348928234
Percentage of Food and Fibre Export
2015Frequency
State
Figure 4: Percentage of Food and Fibre Export 2015

6Statistics for business decisions
Answer to the question (c)
From the analysis and from the above figure it can be concluded that the food
and fibre export except the state Tasmania all the state in 2015 is larger than the
2010.
Similarly, from figure 2 and 3 it is clear that the percentage of food and fibre
export between 2010 and 2015 is not too different (Anscombe, 1973). But in the
state Tasmania, the export is much lower in comparison to the export in 2010.
Solution 2
Class Frequency
Relative
frequency Cumulative frequency Cumulative relative frequency
0 to 4 4 0.1 4 0.1
5 to 9 3 0.075 7 0.175
10 to 14 13 0.325 20 0.5
15 to 19 11 0.275 31 0.775
20 to 24 2 0.05 33 0.825
25 to 29 5 0.125 38 0.95
30 to 34 2 0.05 40 1
Table 1: Class interval
Answer to the question 2 (c)
Figure 5: Histogram on Relative Frequency
0 to 4
5 to 9
10 to 14
15 to 19
20 to 24
25 to 29
30 to 34
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35
0.1
0.075
0.325
0.275
0.05
0.125
0.05
Histogram on Relati ve Frequency
Frequenc
y
Class

7Statistics for business decisions
Answer to the question 2 (d)
0 to 4 5 to 9 10 to 14 15 to 19 20 to 24 25 to 29 30 to 34
0
5
10
15
20
25
30
35
40
4
7
20
31 33
38
Ogive on Weekly sales
Class
Frequency
Figure 6: Ogive on weekly Sales
Answer to the question (e)
The proportion of data less than 20 is 0.775.
Answer to the question (f)
The proportion of data more than 24 is 0.175.

8Statistics for business decisions
Solution 3
Answer to the question (a)
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
1.9
4.6
2.6
0.3
1.3
2.4
5.9
2.93.0
2.42.42.92.5
4.3
2.42.93.3
1.6
2.52.9
1.5
Rate of inflation (%)
Year
Inflation
Figure 7: Trend line of Rate of Inflation (%)
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
Year
Index
Figure 8: Trend line of all - ordinaries index
From figure 7 and 8 it can be concluded that rate of inflation is more fluctuated
than the index during 1995 to 2015 (Johnson and Kuby, 2011). The index variable
shows an increasing trend but the inflation shows a fluctuation trend.

9Statistics for business decisions
Answer to the question (b)
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
Scatter Plot on Inflation Versus Index
Figure 9: Scatter plot
From figure 9 it can be said that between the two variables there is a positive
relationship (St and Wold, 1989). Also, the analysis shows that the relationship is not
that strong.
In the plot the X variable is rate of inflation and the Y variable is index as
because the index is depending upon the rate of inflation.

10Statistics for business decisions
Answer to the question (c)
Rate of inflation
(%)
Mean 2.690476
Standard Error 0.260394
Median 2.5
Mode 2.4
Standard
Deviation 1.193275
Sample Variance 1.423905
Kurtosis 2.038282
Skewness 0.798408
Range 5.6
Minimum 0.3
Maximum 5.9
Sum 56.5
Count 21
Q1 2.15
Q2 2.5
Q3 2.95
Table 2: Summary measure of rate of inflation
All-Ordinaries index
Mean 3982.733
Standard Error 269.9897
Median 4127.6
Mode #N/A
Standard Deviation 1237.248
Sample Variance 1530783
Kurtosis -1.01001
Skewness 0.182747
Range 4336.8
Minimum 2000.8
Maximum 6337.6
Sum 83637.4
Count 21
Q1 2997.5
Q2 4127.6
Q3 5022
Table 3: Summary measure of all ordinaries index

11Statistics for business decisions
Answer to the question (d)
The correlation coefficient between the rate of inflation and the index is 0.039.
Answer to the question (e)
Table 4: Coefficient of regression
The regression model is
Y = 40.31 + 3874.286 * X
Answer to the question (f)
Regression Statistics
Correlation 0.038875116
Coefficient of determination 0.0015
Adjusted R Square -0.05104076
Standard Error 1268.430355
Observations 21
Table 5: Summary table of Regression
The coefficient of determination is 0.0015.
Answer to the question (g)
Null hypothesis: There is no relationship between the rate of inflation and index.
Alternative hypothesis: There is a relationship between the rate of inflation and
index.
ANOVA
df SS MS F Significanc
e F
Regression 1 46268.67733 46268.6
8
0.02875
8
0.87
Residual 19 30569395.73 160891
Coefficients Standard Error t Stat P-value
Intercept
3874.28641
2 696.8319943
5.55985
7
2.31E-
05
X Variable 1
40.3077051
7 237.6901351
0.16958
1
0.86713
2

12Statistics for business decisions
6
Total 20 30615664.41
Table 6: ANOVA table
Test statistic is 0.028, P- Value is 0.87, Alpha value is 0.05 (at 5% level)
P value is larger than the alpha. Thus, the hypothesis is not significant. Hence
it may be concluded at the significance level 5% that is no relationship between the
rate of inflation and index.
Answer to the question (g)
The standard error of the estimate is 696.832
Thus, it is good to fit the regression model.

13Statistics for business decisions
References
Anscombe, F.J., 1973. Graphs in statistical analysis. The American statistician,
27(1), pp.17-21.
Johnson, R.R. and Kuby, P.J., 2011. Elementary statistics. Cengage Learning.
St, L. and Wold, S., 1989. Analysis of variance (ANOVA). Chemometrics and
intelligent laboratory systems, 6(4), pp.259-272.