Assignment Aim: Students are required to show the understanding of the principles and techniques of business research and statistical analysis taught in the course.
Assignment Specifications:
Purpose:
This assignment aims at Understand various qualitative and quantitative research methodologies and techniques, and other general purposes are:
A) Explain how statistical techniques can solve business problems
B) Identify and evaluate valid statistical techniques in a given scenario to solve business problems
C) Explain and justify the results of a statistical analysis in the context of critical reasoning for a business problem solving
D) Apply statistical knowledge to summarize data graphically and statistically, either manually or via a computer package
E) Justify and interpret statistical/analytical scenarios that best fits business solution
Problem 1: Australian food and fibre exports have been on the increase for decades. Among the six Australian states, Victoria leads food and fibre exports. The following table lists the value of food and fibre exports (in millions of dollars) by states in Australia for the years 2010 and 2015. The table is stored in file AUSTRALIAN FOOD AND FIBRE EXPORTS.XLSX (in the course website). Using this data, answer the Problems below.
(a) Use an appropriate graphical technique to compare the amount of food and fibre exports (in millions of dollars) in 2010 and 2015, broken down by the Australian states.
(b) Use an appropriate graphical technique to compare the percentage value of the amount of food and fibre exports (in %) in 2010 and 2015, broken down by the Australian states.
(c) Comment your observations in parts (a) and (b).
Problem 2: The numbers of weekly sales calls by a sample of 40 telemarketers were recorded in the table below.
|
14
|
8
|
6
|
12
|
21
|
4
|
9
|
0
|
25
|
17
|
|
9
|
5
|
8
|
18
|
16
|
3
|
17
|
19
|
10
|
15
|
|
5
|
20
|
17
|
14
|
19
|
7
|
10
|
15
|
10
|
8
|
|
28
|
31
|
27
|
30
|
2
|
17
|
26
|
11
|
29
|
19
|
a. Construct a frequency distribution and a relative frequency distribution for the data.
b. Construct a cumulative frequency distribution and a cumulative relative frequency distribution for the data.
c. Plot a relative frequency histogram for the data.
d. Construct an Ogive for the data.
e. What proportion of the data is less than 20?
f. What proportion of the data is more than 24?
Problem 3: Because inflation reduces the purchasing power of the dollar, investors seek investments that will provide protection against inflation; that is, investments that will provide higher returns when inflation is higher. It is frequently stated that ordinary shares provide just such a hedge against inflation. The annual Australian inflation rate (as measured by percentage changes in the consumer price index) and the annual All-Ordinaries Index from 1995 to 2015 are stored in file INFLATION.XLSX (in the course website).
Using EXCEL, answer below Problems:
a. Using an appropriate graphical descriptive measure (relevant for time series data) describe the two variables.
b. Use an appropriate plot to investigate the relationship between RATE OF INFLATION and ALL- ORDINARIES INDEX. Briefly explain the selection of each variable on the X and Y axes and why?
c. Prepare a numerical summary report about the data on the two variables by including the summary measures, mean, median, range, variance, standard deviation, and coefficient of variation, smallest and largest values, and the three quartiles, for each variable.
d. Calculate the coefficient of correlation (r) between RATE OF INFLATION and ALL-ORDINARIES INDEX. Then, interpret it.
e. Estimate a simple linear regression model and present the estimated linear equation. Then, interpret the coefficient estimates of the linear model.
f. Determine the coefficient of determination R2 and interpret it.
g. Test the significance of the relationship at the 5% significance level.
h. What is the value of the standard error of the estimate (se). Then, comment on the fitness of the linear regression model?
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