Business Statistics Assignment: Data Analysis and Interpretation

This business statistics assignment solution encompasses a wide range of statistical analyses applied to various business scenarios. The assignment begins with exploratory data analysis, including stem and leaf plots and relative frequency histograms, comparing the performance of two companies. It then delves into market capitalization data for companies listed under the ASX and provides investment recommendations based on dividend yields. The solution further explores financial data, calculating descriptive statistics like mean, median, quartiles, and coefficients of variation for several banks and visualizing the data using box and whisker plots. The assignment continues with probability calculations and hypothesis testing, examining rainfall data and student enrollment data, and concludes with normality plots, confidence intervals, and a t-test to determine if there's a significant difference between working capital and total assets of bankrupt and non-bankrupt companies.

Running head: BUSINESS STATISTICS
Business Statistics
Name of the Student:
Name of the Student:
Author’s Note:

2BUSINESS STATISTICS
Table of Contents
Answer 1..............................................................................................................................4
Part 1a..............................................................................................................................4
Part 1b..............................................................................................................................5
Part 1c..............................................................................................................................6
Part 1d..............................................................................................................................7
Answer 2..............................................................................................................................8
Part 2a..............................................................................................................................8
Part 2b..............................................................................................................................8
Part 2c..............................................................................................................................9
Part 2d..............................................................................................................................9
Answer 3............................................................................................................................10
Part 3a............................................................................................................................10
Part 3b............................................................................................................................10
Part 3c............................................................................................................................10
Part 3d............................................................................................................................10
Answer 4............................................................................................................................12
Part 4ai...........................................................................................................................14
Part 4aii..........................................................................................................................14
Part 4bi...........................................................................................................................14

3BUSINESS STATISTICS
Part 4bii..........................................................................................................................14
Answer 5............................................................................................................................15
Part 5a............................................................................................................................15
Part 5b............................................................................................................................17
Part 5c............................................................................................................................18
References..........................................................................................................................20

4BUSINESS STATISTICS
Answer 1
Part 1a
Opening prices for Quarterly data
Year January April July October
2008 13.45 10.5 9.44 9
2009 5.91 6.3 7.3 8.8
2010 8.07 8.08 7.66 8.48
2011 8.37 8.13 8.93 7.8
2012 8.09 8.8 8.57 9.04
2013 1.67 12.3 12 15.54
2014 16.85 16.72 15.1 13.75
2015 12.69 13.3 12.61 10.03
2016 12.5 12.35 12.6 13.06
2017 11.58 11.8 12.15 -
CWN Quarterly opening prices 2008-2017
Year January April July October
2008 6.92 6.4 4.68 3.9
2009 3.27 3.03 3.3 3.35
2010 3.25 3.25 2.95 3.27
2011 3.37 3.53 3.21 2.53
2012 2.68 2.70 2.91 2.68
2013 3.00 3.18 2.95 3.20
2014 3.57 3.33 3.30 3.54
2015 4.08 4.70 4.59 4.7
2016 4.71 4.22 4.55 5.01
2017 4.81 4.77 4.35 -
TAH Quarterly opening prices 2008-2017
The stem and leaf for the two companies can be given as:
Leaves for TAH Stem Leaves for CWN

5BUSINESS STATISTICS
0 6 6 7 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9
1 0 1 1 2 2 2 2 2 2 3 3 3 3 3 3 3 4 5 6 7 7
9 9 7 7 7 5 2
9 6 5 5 4 3 3 3 3 3 3 3 3 2 2 2 2 0 0 0 3
8 8 7 7 7 7 6 6 4 2 1 4
0 5
9 4 6
Stem and Leaf Display
Part 1b
CWN plotted as relative frequency histogram
TAH plotted as relative frequency polygon
 Frequency/ Total Frequency = Relative Frequency
The following interval will be starting from $0 to less than $2
Opening prices CWN (Relative Frequency) TAH (Relative Frequency)
$0 to less than $2 0.000 0
$2 to less than $4 0.000 0.641
$4 to less than $6 0.000 0.308
$6 to less than $8 0.128 0.051
$8 to less than $10 0.333 0
$10 to less than $12 0.128 0
$12 to less than $14 0.308 0
$14 to less than $16 0.051 0
$16 to less than $18 0.051 0
CWN and TAH and their Relative Frequencies

6BUSINESS STATISTICS
$0 to less
than $2 $2 to less
than $4 $4 to less
than $6 $6 to less
than $8 $8 to less
than $10 $10 to less
than $12 $12 to less
than $14 $14 to less
than $16 $16 to less
than $18
0.000
0.050
0.100
0.150
0.200
0.250
0.300
0.350
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
CWN and TAH
CWN TAH
Opening prices
Frequency
CWN and TAH and their Relative Frequencies
Part 1c
The market capital for the five companies under ASX can be given as:
Companies Listed under ASX Market Capitalisation (Over AUD
500M)
Aristrocat Leisure Limited (ALL) 13518
Crown Resorts Limited (CWN) 8039
Fairfax Media Limited (FXJ) 2219
Flight Centre Travel Group Limited (FLT) 4885
Tabcorp Holdings Limited (TAH) 3432
The Star Entertainment Group Limited (SGR) 4293
Companies Listed under ASX and their Market Capitalisation

7BUSINESS STATISTICS
ALL
CWN
FXJ
FLT
TAH
SGR
0 2000 4000 6000 8000 10000 12000 14000 16000
Market Capitalisation for leisure and entertainment
companies in million AUD
Market Capital (AUD Million)
Companies Listed under ASX
Companies Listed under ASX and their Market Capitalisation
Part 1d
As per the data given in InvestSMART (2017) for “peer comparison”, based on Market
Capitalisation, Growth and Dividend Yield, it is better to invest in Crown Resorts (CWN)
because shareholders have received more dividend in 2017 than in Tabcorp (TAH) and is
subjected to receive likewise the same in upcoming years

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Answer 2
Part 2a
The mean, median and quartiles for the prices of each publisher can be given as:
CBA NAB ANZ WBC
Mean $3.10 $2.31 $2.06 $2.04
Q1 2.49 2.1875 1.91 1.907
Median $3.05 $2.36 $2.05 $2.04
Q3 3.7325 2.45075 2.173 2.2355
Min $2.49 $2.19 $1.91 $1.91
Max $3.73 $2.45 $2.17 $2.24
Mean, Quartiles and Median for each bank
As per the data calculated, the annual dividends have been given maximum by CBA as
per the mean and median data followed by NAB. Also, Q1 and Q3 is even higher for CBA.
Part 2b
CBA NAB ANZ WBC
Range (Max-Min value) $2.23 $0.79 $1.21 $1.30
Coefficient of Variation (sd/ x̅ * 100) $25.40 $9.86 $17.38 $18.03
Standard Deviation 0.787482
0.22795367
7 0.358824
0.36718812
9
Each Bank’s Range, SD and Coefficient of Variation
.

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Part 2c
CBA NAB ANZ WBC
0
0.5
1
1.5
2
2.5
3
3.5
4
Box and Whister Plot Banks
Q3-Median
Median-Q1
Q1
Banks
Annual Dividends per share
Box and Whisker Plot for each Bank
Part 2d
APRA has increased the pressure on banks primarily for the reason that these four largest
banks have a high capital surplus above the minimum requirements such that these minimum
requirements would be added with 150 base point’s benchmark to find extra capital. Also, this is
done to enable banks handle adversity in the times of need without endangering its core objective
of financial intermediation for Australian society (White, 2017).

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Answer 3
Part 3a
Discipline being most popular for best students is “Engineering and Related
Technologies”
 Proportion = 4203/ 14027 = 0.299636
Part 3b
P (Society and Culture and ATAR 80 and less) = 5030/ 25262 = 0.1991132
Part 3c
Field of education 50.00 or
less
proportion with lowest ATAR
rate
Natural and Physical Sciences 705 705/ 9723 = 0.072508485
Information Technology 418 418/ 9723 = 0.042990846
Engineering and Related Technologies 289 289/ 9723 = 0.029723336
Architecture and Building 316 316/ 9723 = 0.032500257
Agriculture, Environmental and Related Studies 98 98/ 9723 = 0.010079194
Health 1,568 1568/ 9723 = 0.161267099
Education 1,062 1062/ 9723 = 0.109225548
Management and Commerce 1,742 1742/ 9723 = 0.17916281
Society and Culture 2,814 2814/ 9723 = 0.289416847
Creative Arts 683 683/ 9723 = 0.070245809
Total 9,723
P (Highest proportion of students with lowest ATR grades) = 2814/ 9723 = 0.289416847
(Society and Culture)
Part 3d
Field of education No ATAR/
Non-Yr 12
majority
Natural and Physical Sciences 7,434 7,434/ 91,567 = 0.081186454
Information Technology 2,281 2,281/ 91,567 = 0.024910721

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Engineering and Related Technologies 3,719 3,719/ 91,567 = 0.040615069
Architecture and Building 2,634 2,634/ 91,567 = 0.028765822
Agriculture, Environmental and Related Studies 1,271 1,271/ 91,567 = 0.013880546
Health 31,341 31,341/ 91,567 =
0.342273963
Education 7,077 7,077/ 91,567 = 0.077287669
Management and Commerce 10,331 10,331/ 91,567 =
0.112824489
Society and Culture 18,161 18,161/ 91,567 =
0.198335645
Creative Arts 6,764 6,764/ 91,567 = 0.073869407
Total 91,567
The maximum number of students from “No ATAR/Non-Yr 12” background is Health.
Generally, health and scirnces are with No ATAR background because they are based on
learning and academic performance to satisfy course prerequisites in their undergraduate course
(Futurestudents.unimelb.edu.au., 2012).

12BUSINESS STATISTICS
Answer 4
Rainfall In Adelaide, South Australia in 2016
Week Number of Rainfall events Total Rainfall Std. Dev
1 0 0 0
2 1 1.2 0.453557368
3 3 16.4 3.732227727
4 3 18.6 4.794043924
5 2 13.8 4.050396806
6 0 0 0
7 1 0.6 0.226778684
8 1 0.4 0.151185789
9 0 0 0
10 3 31.8 7.901657451
11 1 9 3.401680257
12 1 0.8 0.302371578
13 0 0 0
14 1 4.4 1.663043681
15 1 0.2 0.075592895
16 1 0.6 0.226778684
17 3 3.2 0.957178393
18 2 6.6 2.087148887
19 5 14.6 4.31564154
20 1 0.2 0.075592895
21 6 41 7.949603165
22 5 7.8 1.365562853
23 7 20.6 2.794552524
24 2 4.2 1.341640786
25 5 33.2 5.901089488
26 4 11.4 2.127372625