Statistical Analysis and Data Visualization

This assignment focuses on statistical concepts like hypothesis testing, confidence intervals, and data visualization. It includes a scenario involving machine profits, where students need to conduct a hypothesis test and calculate a confidence interval. Additionally, it explores the use of back-to-back histograms to compare categorical and numerical variables, providing an example using male and female salaries. The assignment also delves into sampling distributions and estimation techniques.

Running Head: BUS105 COMPUTING ASSIGNMENT SEMESTER 3, 2017
BUS105 COMPUTING ASSIGNMENT SEMESTER 3, 2017
Name of the Student
Student Number
Allocated Sample: 1

1BUS105 COMPUTING ASSIGNMENT SEMESTER 3, 2017
Executive Summary
The aim of this study is to understand the different techniques that can be applied to compare
different types of variables. The first section involves definitions and the rest of the sections that
follow include the application of different techniques for the purpose of comparison of the given
variables.

2BUS105 COMPUTING ASSIGNMENT SEMESTER 3, 2017
Table of Contents
Section 1..........................................................................................................................................5
Section 2..........................................................................................................................................6
Part A...........................................................................................................................................6
Part B...........................................................................................................................................6
Part C...........................................................................................................................................6
Part D...........................................................................................................................................7
Part E...........................................................................................................................................7
Section 3..........................................................................................................................................8
Part A...........................................................................................................................................8
Part B...........................................................................................................................................8
Part C...........................................................................................................................................9
Part D...........................................................................................................................................9
Answer (i)................................................................................................................................9
Answer (ii)...............................................................................................................................9
Answer (iii)..............................................................................................................................9
Answer (iv)..............................................................................................................................9
Part E...........................................................................................................................................9
Answer (i)................................................................................................................................9
Answer (ii).............................................................................................................................10

3BUS105 COMPUTING ASSIGNMENT SEMESTER 3, 2017
Answer (iii)............................................................................................................................10
Answer (iv)............................................................................................................................10
Section 4........................................................................................................................................11
Part A.........................................................................................................................................11
Part B.........................................................................................................................................11
Part C.........................................................................................................................................11
Answer (i)..............................................................................................................................11
Answer (ii).............................................................................................................................11
Answer (iii)............................................................................................................................11
Answer (iv)............................................................................................................................12
Part D.........................................................................................................................................12
Answer (i)..............................................................................................................................12
Answer (ii).............................................................................................................................12
Answer (iii)............................................................................................................................12
Answer (iv)............................................................................................................................12
Section 5........................................................................................................................................13
Section 6........................................................................................................................................14
Part A.........................................................................................................................................14
Part B.........................................................................................................................................14
Part C.........................................................................................................................................14

4BUS105 COMPUTING ASSIGNMENT SEMESTER 3, 2017
Answer (i)..............................................................................................................................14
Answer (ii).............................................................................................................................14
Answer (iii)............................................................................................................................15
Part D.........................................................................................................................................15

5BUS105 COMPUTING ASSIGNMENT SEMESTER 3, 2017
Section 1
A dataset is a collection of data that involves different variables of different types. These
variables contain values which are known as data. For example, the collection of information of
the students names, the classes to which they belong and the marks obtained by each of them in
each of the subjects can be termed as a dataset. Each of the characteristics such as students
names, classes, marks are known as variables.
The values of the variables changes with the change in situation. For example, in the
example stated above, the marks of the students are different for each of the student. There are
two types of variables – Qualitative variable and Quantitative variable. Qualitative variable are
the variables that records qualitative data. In this example discussed above, the class of the
students is a qualitative variable. Quantitative variables can be discrete and continuous. Discrete
variables are the variables which possess countable values and continuous variables are the
variables which possess uncountable values. Here, “marks” is a continuous variable.
Datasets are usually summarized with the help of computers as the computations become
very easy and less time consuming. Relationship between two quantitative variables can be
shown with a scatter diagram, a qualitative and a quantitative variable can be compared by
computing their mean values and two qualitative variables can be compared by computing their
proportions.

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Section 2
Part A
15000 20000 25000 30000 35000 40000 45000
0
2000
4000
6000
8000
10000
12000
14000
16000
18000
20000
f(x) = − 0.292227028680095 x + 22199.7051551869
Scatterplot
Distance Travelled
Selling Price
The figure shows that selling price and distance has a negative relationship. The selling
price of a car decreases with the increase in the distance travelled by the car. The relationship to
estimate the selling price of a car can be given by the following equation:
Selling Price = (-0.2922 * Distance Travelled) + 22200
Part B
The selling price of a car that has travelled 30,000 km can be estimated as:
Selling Price = (-0.2922 * 30000) + 22200 = $13,434
Part C
It is given that the average of 10,000 estimates is 14000 and standard deviation is 392. The
required z-score for sample 1 estimate is (13434 – 14000) / 392 = -1.44

7BUS105 COMPUTING ASSIGNMENT SEMESTER 3, 2017
Part D
Using wolframalpha.com, P (Z <-1.44) = 0.0749
Part E
The expected rank of sample 1 in comparison with 10,000 samples is
Expected Rank = P (Z < z-score) * 10000 = 0.0749 * 10,000 = 749

8BUS105 COMPUTING ASSIGNMENT SEMESTER 3, 2017
Section 3
Part A
which sample ? 1
Count of Do they like it ? (y=yes, n=no) Column Labels
Row Labels n y
Grand
Total
A 9 97 106
B 20 68 88
Grand Total 29
16
5 194
which sample ? 1
Count of Do they like it ? (y=yes, n=no) Column Labels
Row Labels n y
Grand
Total
A 8.49%
91.51
% 100.00%
B 22.73%
77.27
% 100.00%
Grand Total 14.95%
85.05
% 100.00%

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Part B
A B
0.00%
20.00%
40.00%
60.00%
80.00%
100.00%
120.00%
8.49% 22.73%
91.51% 77.27%
Comparison of Proportions
y
n
Version
Proportion
Part C
Preference is given to version A over version B as can be seen from the results in parts A and B
Part D
Answer (i)
The estimated difference in proportion using sample 1 is 0.9151 – 0.7727 = 0.1424
Answer (ii)
The average of 1000 sample estimates is 0.1 with standard deviation 0.0505. Therefore, the z-
score for that estimate in sample 1 is (0. 1424 - 0.1) / 0.0505 = 0.84
Answer (iii)
Using wolframalpha.com, P (Z < 0.84) = 0.7995
Answer (iv)
Comparing sample 1 to the 1000 samples, the expected rank can be obtained as:

10BUS105 COMPUTING ASSIGNMENT SEMESTER 3, 2017
Expected Rank = P (Z < z-score) * 1000 = 0.7995 * 1000 = 799
Part E
Answer (i)
Here, H0 and H1 are defined as:
H0: p1=p2
H1: p1 ≠p2
Here, p1 and p2 are the proportions preferring version A and B respectively.
Answer (ii)
The p-value has been obtained as 0.0056
Answer (iii)
H0 is rejected
Answer (iv)
The variable is statistically significant and hence, the two sample proportions are not equal.

11BUS105 COMPUTING ASSIGNMENT SEMESTER 3, 2017

12BUS105 COMPUTING ASSIGNMENT SEMESTER 3, 2017
Section 4
Part A
which
sample? 1
Values
Row Labels
Count of which machine?
(A or B)
Average of $ Casino profit
from bet
StdDev of $ Casino profit
from bet
A 98 0.448979592 4.381597997
B 102 0 1.421197376
Grand
Total 200 0.22 3.230134493
Part B
The average profit from machine A is $0.45 with a standard deviation of 4.38 which is quite
high. Thus, the profits on each run are not always close to the average profit. On the other hand,
the profit and loss from machine B nullifies each other and there is no average profit from
machine B.
Part C
Answer (i)
Using sample 1, the estimate for the difference between the sample means is (0.45 – 0) = 0.45
Answer (ii)
The average of the 2000 sample estimates is 0.4 with standard deviation 0.46
so the z-score of the sample 1 estimate is = (0.45 – 0.4)/0.46 = 0.11
Answer (iii)
Using wolframalpha.com, P (Z < 0.11) = 0.5438

13BUS105 COMPUTING ASSIGNMENT SEMESTER 3, 2017
Answer (iv)
Comparing sample 1 to the 1000 samples, the expected rank to which the sample will be close to
is:
Expected Rank = P (Z < z-score) * 1000 = 0.5438 * 1000 = 543
Part D
Answer (i)
Here, H0 and H1 are defined as:
H0: μ1 - μ2 = 0
H1: μ1 - μ2 ≠ 0
Here, μ1 and μ2 are the average profits from machines A and B respectively.
Answer (ii)
The p-value has been obtained as 0.3257
Answer (iii)
H0 is accepted
Answer (iv)
The mean profits from both the machines A and B are equal

14BUS105 COMPUTING ASSIGNMENT SEMESTER 3, 2017
Section 5
An example of a back to back histogram is given below:
In the figure, the green bar shows the number of males and the brown bar shows the number of
females and comparison is done on the male and female salaries of a company. Here income is
numerical and gender is categorical. Thus, this is a way in which a categorical variable and a
numerical variable can be compared.
This type of graph can be used by various businesses to show comparisons of various
factors.

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Section 6
Part A
sample 1
Column Labels
no yes
Grand
Total
Count of do you support proposed
change? 81
12
5 206
sample 1
Column Labels
no yes
Grand
Total
Count of do you support proposed
change? 0.393203883
0.60679611
7 1
Part B
The sample size for sample 1 is 206 and the sample proportion of the people that support the
change is (125/206) = 0.6068
Part C
Answer (i)
The average of the 1000 estimates is 0.6 with standard deviation 0.0357. So, the z-score of the
sample 1 estimate is = (0. 6068 – 0.6)/0.0357 = 0.19
Answer (ii)
Using wolframalpha.com P (Z < 0.19) = 0.5753

16BUS105 COMPUTING ASSIGNMENT SEMESTER 3, 2017
Answer (iii)
If we compare the sample 1 to the 1000 other estimates, then we estimate the rank to be 0.5753 *
1000 = 575
Part D
A 95% confidence interval for the proportion of people that support the change is given by
(0.5401, 0.6735)