STATISTICS CALCULATION

Instructions
ECMT1010 Written Assignment
Due Friday June 8, 2012, 4:30pm
 In order to complete this assignment, you will need the following data sets:

1. Fiji farm survey.xls
2. Australian retail turnover.xls
3. Dairy.xls
4. Top 1000.xls
5. Queensland tourism.xls
6. ARIA.xls

 This assignment must be done alone and is worth 10% of your final mark.

 You will be marked on the correctness of your answers as well as presentation.

 Late assignments will be penalised 20% of full marks per day.

 The assignment must be submitted both electronically and by hard-copy.  The hardcopy
version
is
to
be
submitted
into
the
assignment
boxes
on level
2 of
the

Merewether
Building.
The
electronic
version
must
be
submitted
via
the
University

Learning
Management
System
(see
3
minute
online
tutorial
for
further
details).

 You should familiarise yourself with the University’s policies regarding academic
honesty and plagiarism and understand the following declaration:

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Assignment Questions
1.  (Chapter 2, Analysing the Data Sets Problem 2)
For the Fiji farm survey data set, produce a histogram for the variable ‘Education’. Interpret
you results and explain any grouping in the histogram
2.  (Chapter 2, Analysing the Data Sets Problem 3)
Using the Australian retail turnover data set, produce a scatter plot of the turnovers for food
retailing and department stores. Comment on your findings.
3.  (Chapter 2, Analysing the Data Sets Problem 4)
For the Dairy data set, produce a Pareto chart for the state-wide production of milk in 2007–
08.

4.  (Chapter 3, Analysing the Data Sets Problem 1)
Access the Top 1000 data set.

a.   Calculate the descriptive statistics for net profit, total revenue, and number of
employees.

b.   What conclusions can you reach from the comparison of net profit and revenue
distributions? Calculate the coefficient of variation for each distribution and comment
on the variability of the two distributions.

c.   Calculate the descriptive statistics for return on funds and return on revenue. Comment
on the distribution.
5.  (Chapter 4, Analysing the Data Sets Problem 2)
In the Fiji farm survey data set:

a.   What is the probability that a randomly selected farmer has a cane output of 300
tonnes?

b.   What is the probability that a randomly selected farmer has cultivated an area of 10
acres?

c.   What is the probability that a randomly selected farmer is a part-time farmer and has a
cane output of 300 tonnes?

d.   What is the probability that a randomly selected farmer is a part-time farmer and over
55 years of age?

e.   What is the probability that a randomly selected farmer is neither a part-time farmer
nor over 55 years of age?

6.  (Chapter 5, Analysing the Data Sets Problem 1)
Use the Queensland tourism data set. What is the probability that a randomly selected
Queensland hotel room was occupied in September 2003? Use this as the value of p a
binomial experiment and assume it is the current rate of occupancy. If you were to randomly
select 10 hotel rooms in Queensland, what is the probability that no more than five are
occupied? If you were to randomly select 20 hotel rooms in Queensland, what is the
probability that no more than 10 are occupied?

7.  (Chapter 6, Analysing the Data Sets Problem 2)
Use the Fiji farm survey data set; noting that the cultivated area variable is nearly normally
distributed. What is the probability that the area of a cultivated sugar cane farm selected at
random is less than ten acres?
8.  (Chapter 7, Analysing the Data Sets Problem 2)
Refer to the data for room occupancy rates for licensed hotels in the Queensland tourism data
set. The room occupancy rate for the December quarter 2007 was 71.8%. Assume that this
figure is typical for occupancy rates for this time of the year. If you randomly selected 50
licensed hotels, what is the probability that you will get a room occupancy rate for the
December quarter 2007 that is less than 60%? What is the probability that you will get a
room occupancy rate for the December quarter 2007 of between 80% and 90%?
9.  (Chapter 8, Analysing the Data Sets Problem 1)
Using the Fiji farm survey data set, construct a 95% confidence interval for the population
mean cane output per farmer. Also construct a 95% confidence interval for population mean
cane output per acre. Comment on the results.
10.  (Chapter 9, Analysing the Data Sets Problem 4)
Using the Top 1000 data set, test whether the mean return on revenue is less than 20%.
Assume σ is unknown, then repeat the test assuming σ = 22. Use α = 5%. What do you
conclude?

11.  (Chapter 10, Analysing the Data Sets Problem 1)
Using the Fiji farm survey data set, test whether the mean output per farmer is the same for
land owned and land not owned. Use a level of significance 5%.
12.  (Chapter 13, Analysing the Data Sets Problem 1)
Develop a regression model from the ARIA data set to predict sales of CD albums from the
sales of CD singles. Discuss the model and its strength on the basis of indicators presented in
this chapter. Does it seem logical that unit sales of CD albums could be predicted by CD
singles sales?

SOLUTION

LI43

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