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:

By submitting an assignment through the University Learning Management System,

1. I certify that: I have read and understood the University of Sydney Academic

Dishonesty and Plagiarism Policy;

2. I understand that failure to comply with the above can lead to the University

commencing proceedings against me for potential student misconduct under

Chapter 8 of the University of Sydney By-Law 1999 (as amended);

3. This Work is substantially my own, and to the extent that any part of this Work

is not my own, I have indicated that it is not my own by acknowledging the

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4. I declare that this assignment is original and has not been submitted for

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Information on plagiarism is available online at:

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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

000’s | CDs Single | CDs Album | |||||||||||||||

1998 | 9900 | 39631 | |||||||||||||||

1999 | 11290 | 42672 | |||||||||||||||

2000 | 11099 | 43917 | |||||||||||||||

2001 | 12367 | 49670 | |||||||||||||||

2002 | 11343 | 46954 | |||||||||||||||

2003 | 9464 | 50640 | |||||||||||||||

2004 | 9286 | 48234 | |||||||||||||||

2005 | 7394 | 46174 | |||||||||||||||

2006 | 4331 | 49818 | SUMMARY OUTPUT | ||||||||||||||

2007 | 2498 | 44045 | |||||||||||||||

Regression Statistics | |||||||||||||||||

Multiple R | 0.053393725 | ||||||||||||||||

R Square | 0.00285089 | ||||||||||||||||

Adjusted R Square | -0.121792749 | ||||||||||||||||

Standard Error | 3786.019971 | ||||||||||||||||

Observations | 10 | ||||||||||||||||

ANOVA | |||||||||||||||||

df | SS | MS | F | Significance F | |||||||||||||

Poor regression equation having very low R^2 value. | Regression | 1 | 327850.7 | 327850.7 | 0.022872 | 0.883534 | |||||||||||

Thus the model is not a good fit for the equation | Residual | 8 | 1.15E+08 | 14333947 | |||||||||||||

Total | 9 | 1.15E+08 | |||||||||||||||

Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | ||||||||||

Intercept | 46700.57547 | 3672.526 | 12.7162 | 1.38E-06 | 38231.71 | 55169.44 | 38231.71 | 55169.44 | |||||||||

X Variable 1 | -0.05901581 | 0.390223 | -0.15124 | 0.883534 | -0.95887 | 0.840841 | -0.95887 | 0.840841 |

LI43

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