BUS105 Computing Assignment Semester 3, 2017: Variable Comparison

This document presents a computing assignment solution for the BUS105 course, focusing on data analysis and variable comparison techniques. The assignment explores different types of variables, including qualitative and quantitative, and demonstrates the application of various statistical methods. It covers topics such as calculating z-scores, comparing proportions, and hypothesis testing. The solution includes examples of comparing variables using scatter diagrams, calculating mean values, and determining proportions. The assignment also presents examples of back-to-back histograms to compare categorical and numerical variables. The student analyzes datasets, calculates confidence intervals, and interprets the results. Furthermore, the assignment covers the interpretation of p-values and the acceptance or rejection of null hypotheses.

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

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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

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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.

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