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University of New England

Faculty of The Professions

School of Business, Economics and Public Policy

QM162/262

Business Statistics 2

Assessment

Dr Rene Villano

Semester 2, 2010

. University of New England 2010

CRICOS Provider No: 00003G

Assessment Summary

QM162/262

Business Statistics 2

Assignment 1

Due date: August 23, 2010

Assignment 2

Due date: September 27, 2010

Assignment 2

Due date: October 18, 2010

Table of Contents

Assessment Submission .................................................................................................. 1

Submission method ........................................................................................ 1
TurnItIn .......................................................................................................... 1
AskUNE ......................................................................................................... 1
Plagiarism declaration .................................................................................... 2
Assignment cover sheets ................................................................................ 2
Assessment Details and Marking Policy ....................................................................... 3
Assessment details ................................................................................................... 3
Overview of assessment requirements ........................................................... 3
Assessment details ......................................................................................... 3
Examination ................................................................................................... 3
Tutorials ......................................................................................................... 3
Assignments ................................................................................................... 4
Assignment 1 ................................................................................................. 5
Marking policy ...................................................................................................... 14
Plagiarism .................................................................................................... 14
Assessment preview ..................................................................................... 14
Casual markers and moderation process ...................................................... 14
Extensions and late submission ................................................................... 14
Return of assessments .................................................................................. 15
Re-marking of assessments tasks ................................................................. 15
Assessment Information ............................................................................................... 16
Assessment policy ........................................................................................ 16
Plagiarism .................................................................................................... 16
UNE grading system .................................................................................... 17
Examinations................................................................................................ 18
Appeals ........................................................................................................ 19
AskUNE ....................................................................................................... 19
Tutorial Exercises ......................................................................................................... 20
Tutorial 1 ............................................................................................................... 20
Exercise 1.1 .................................................................................................. 20
Exercise 1.2 .................................................................................................. 20
Exercise 1.3 .................................................................................................. 20
Tutorial 2 ............................................................................................................... 22
Exercise 2.1 (Two large independent samples) ........................................... 22
Exercise 2.2 (Two small independent samples) ........................................... 22
Tutorial 3 ............................................................................................................... 24
Exercise 3.1 .................................................................................................. 24
Exercise 3.2..................................................................................................24Exercise 3.3..................................................................................................25Exercise 3.4..................................................................................................25Tutorial 4...............................................................................................................28Exercise 4.1..................................................................................................28Exercise 4.2:Testing for Differences of 2 Population Proportions..........28Tutorial 5...............................................................................................................31Exercise 5.1:Testing for Differences of more than 2 Population
Proportions31Tutorial 6...............................................................................................................33Exercise 6.1..................................................................................................33Exercise 6.2: Small Sample Test.................................................................35Exercise 6.3:Large Sample Test.................................................................36Tutorial 7...............................................................................................................37Exercise 7.1..................................................................................................37Exercise 7.2..................................................................................................38Tutorial 8...............................................................................................................39Tutorial 9...............................................................................................................40Exercise 9.1..................................................................................................40Tutorial 10.............................................................................................................43Exercise 10.1................................................................................................43Exercise 10.2................................................................................................43Tutorial 11.............................................................................................................45Exercise 11.1:Index Numbers.....................................................................45Tutorial 12.............................................................................................................46Exercise 12.1: Poisson Distribution.............................................................46Exercise 12.2: Exponential Distribution......................................................46

Assessment Submission
Submission method
Assessment tasks for this unit must be submitted electronically via the University's
e-Submission system.
e-Submission is accessible through the myUNE student portal or by clicking on the
e-Submission link in your online unit.
Once your assignment has been e-submitted for marking, it will be submitted to
TurnItIn for final checking by UNE. This will generate a report for the unit coordinator.

Assignments must be submitted by 23.59. Your assignment’s receipt date/time is
recorded automatically. You must take into account time zone differences to avoid
penalties for late submission.

Please note that you can only submit ONE file per assignment and that you are only
able to submit each assignment ONCE.

If you require assistance with the e-submission of your assignment, contact the IT
Service Desk on 02 6773 5000 or email servicedesk@une.edu.au.

TurnItIn

UNE uses a software application to determine the originality of assessable work
submitted by its students. This software is called TurnItIn and it is part of the
e-submission process.

In order that you may use TurnItIn as an educative tool, the e-submission process
allows you to submit your assignment to TurnItIn for checking before you submit it for
marking. This is an optional step and can occur as many times as you require in order to
receive a satisfactory report. Once you are satisfied with your report, you will then
submit your assignment for marking.

When a file is submitted to TurnItIn, the software compares the text in the submitted
files with text from a range of electronic sources including online journals, online
databases, the Internet and the TurnItIn database. Any strings of text that occur in both
the submitted document and in one or more of the electronic sources are identified by
the software with a unique number and colour in what TurnItIn calls the 'originality
report'.

More information about e-Submission and TurnItIn can be found at
http://www.une.edu.au/tlc/learningresources/esub-tii-student.htm.

AskUNE

If you require further clarification regarding e-Submission or TurnItIn, you can browse
the frequently asked questions at AskUNE, or ask a question of your own by clicking on
the ‘Contact Us’ tab.

Plagiarism declaration

When you submit an assignment via e-Submission, you will be deemed, in effect, to
have agreed to the UNE plagiarism policy.

Assignments submitted in hard copy must include a signed plagiarism declaration form,
which is included on the assignment cover sheet.

Assignment cover sheets

e-Submitted assignments do not require assignment cover sheets as these are generated
automatically by the e-Submission system when you submit your assignment.

All assignments that are submitted in hard copy must have an assignment cover sheet
attached. These can be accessed from myUNE, by clicking on the 'myStudy' tab and
then on the icon in the Assignments list. If you have received an exemption from the
requirement to have computer access, you will receive your assignment cover sheets in
the mail.

Assignments that are being submitted in hard copy should be mailed to:

Assignment Section
Teaching & Learning Centre
University of New England
Armidale NSW 2351

Assessment Details and Marking
Policy

Assessment details

Overview of assessment requirements

This unit will be assessed on the basis of three (3) assignments, a 2-hour final
examination at the end of the semester. Internal students are required to attend tutorial
sessions, which carry 5% of the final marks. In order to pass the unit, the student must
obtain an aggregate mark of 50%.

Tasks

External
Students

(%)

Internal
Students

(%)

Assignments (3)

Tutorial Exercises

Final Examination (2-hours)

Total

100

Assessment details

Examination

The 2-hour final exam will contribute 70% (E) and 65% (I) to your final assessment.
No notes or books will be permitted in the exam. Calculators may be used and will be
needed. A set of potentially useful statistical formulae and tables will be provided in
the exam. Students enrolled in QM 262 will be required to answer an additional
question on the exam.

Additional information will be forwarded to all students on Week 7.

For information regarding exam dates, exam results, timetables, on and off-campus
exams, exam centres and codes, overseas costs, and changing your nominated exam
centre please visit: http://www.une.edu.au/exams/examtimetable.htm.

Tutorials

Tutorials are compulsory for internal students. You will be required to submit random
exercises questions, which would constitute the 5% of the assessment. If the question

requires computer output, you are expected to produce and bring them to your allocated
tutorial sessions. Some of these will be randomly collected. Tutorial questions are listed
on the tutorial exercises section of this file.

Assignments

There are three (3) assignments for this unit.

The assignments are intentionally designed to (a) review material, (b) extend material
and (c) discriminate between students. I expect you will find some of the questions
straightforward and others more challenging.

Deadlines for e-submission of assignments are as follows:

Topics
Covered

Assign
No.

Description

Posting Date

1 and 2

Two-sample tests and Analysis of
Variance

August 23, 2010

3 and 4

Chi-square tests and multiple regression

September 27, 2010

5 and 6

Time-series forecasting and index numbers

October 18, 2010

Your answers to each assignment should be submitted along with any associated
workings, in the form of calculations and computer printouts. Marks for assignments
will be allocated according to logical structure and method (70%), accuracy of results
(20%) and presentation (10%).

For all questions requiring statistical test procedures, you are expected to clearly state
the following:

(a) The null and alternative hypotheses
(b) The test statistic used (algebraic expression)
(c) Any assumptions made
(d) Value of the test statistic (you can obtain this from the computer output)
(e) P-Value (if available)
(f) Decision Rule
(g) Decision
(h) Conclusion (in words)

Data can be downloaded from the unit Blackboard or can be accessed from your CD-ROM.

Assignment 1

Due Date: August 23, 2010

QM 162/262 (100 marks)

Weight: 10%

Question 1 (20 Marks)

The operation manager at the light bulb factory wants to determine whether there is any
difference in the average life expectancy of bulbs manufactured on two different types
of machines. The process standard deviation of Machine 1 is 110 hours and of Machine
II is 125 hours. A random sample of 25 light bulbs obtained from Machine 1 indicates a
sample mean of 375 hours, and a similar sample of 25 from Machine II indicates a
sample mean of 362 hours.

(a) Using the 0.05 level of significance, is there any evidence of a difference in the
average life of bulbs produced by the two types of machines?
(b) Report the p-value in (a) and interpret its meaning.

Question 2 (30 Marks)

A sporting goods manufacturing company wanted to compare the distance travelled by
golf balls produced by each of four different designs molds. Ten balls were
manufactured with each design and were brought to the local golf course for the club
professional to test. The order in which the balls were hit with a driver from the first tee
was randomized so that the pro did not know which design was being hit. All 40 balls
were hit in a short period of time, during which the environment conditions were
essentially the same. The results (distance travelled in yards) for the four designs were
as follows: (GOLFBALL.XLS is available in the CD ROM)

Design 1

Design 2

Design 3

Design 4

206.32

217.08

226.77

230.55

207.94

221.43

224.79

227.95

206.19

218.04

229.75

231.84

204.45

224.13

228.51

224.87

209.65

211.82

221.44

229.49

203.81

213.9

223.85

231.1

206.75

221.28

223.97

221.53

205.68

229.43

234.3

235.45

204.49

213.54

219.5

228.35

210.86

214.51

233

225.09

(a) At the 0.05 level of significance, is there evidence of differences in the average
distance travelled by the golf balls produced from the four design molds?
(b) If the results you obtained in (a) indicate that it is appropriate, used the Tukey-
Kramer procedure to determine which groups differ in average distance.
(c) What assumptions are necessary in (a)? Do you think these assumptions are
valid for these data? Explain.

To use Excel

Click Data | Data Analysis | ANOVA-Single Factor | (enter the required data)

Click Add-ins| PHStat | Mutliple Sample Test | Tukey-Kramer Procedure | (enter the required information that follows)

Question 3 (30 Marks)

The effects of developer strength (factor A) and development time (factor B) on the
density of photographic plate film were being studied. Two strengths and two
development times were being used, and four replicates for each treatment combination
were run. The results, with the larger results being best, are as follows: (PHOTO.XLS)

Developer Strength

Development Time (Minutes)

(a) At the 0.05 level of significance, is there an interaction between developer
strength and development time?
(b) At the 0.05 level of significance, is there an effect due to developer strength?
(c) At the 0.05 level of significance, is there an effect due to development time?
(d) Plot a graph of mean density of each developer strength for development time.
(e) What can you conclude about the effect of developer strength and development
times on density?

To use Excel

Click Tools |Data Analysis | ANOVA-Two Factor with Replication | (enter the required data)

Use Chart Wizard to plot the graph.

Question 4 (20 Marks)

An operation manager in a company that manufactures electronic audio equipment is
inspecting a new type of battery. A batch of 20 batteries is randomly assigned to four
groups (so that there are 5 batteries per group). Each group of batteries is then
subjected to a particular pressure level low, normal, high, or very high. The batteries

are simultaneously tested under these pressure levels, and the following times to failure
(in hours) are recorded: (PRESSURE.xls data available for download from
blackboard)

PRESSURE

Low

Normal

High

Very High

8.0

7.6

6.0

5.1

8.1

8.2

6.3

5.6

9.2

9.8

7.1

5.9

9.4

1.9

7.7

6.7

11.7

12.3

8.9

7.8

The operations manager, by experience, knows that such data come from populations
that are not normally distributed, and he wants to use a nonparametric procedure for
purposed of data analysis.

(a) At 0.05 level of significance analyse the data to determine whether there is
evidence of a significant difference between the four pressure levels with respect
to median battery life.
(b) Based on your results in (a), recommend a warranty policy with respect to
battery life. (Maximum 250 words).

To use Excel

Click Add-Ins| PHStat | Multiple-sample test | Kruskal-Wallis Test | (enter the required information)

Assignment 2

Due Date: September 27, 2010

QM 162 (100 marks)

QM 262 (125 Marks)

Weight: 10%

Question 1 (25 Marks)

A company that produces and markets videotaped continuing education programs for
the financial industry has traditionally mailed sample tapes to prospective customers
that contain previews of the programs. Customers then agree to purchase the program
tapes or return the sample tapes to the sales representatives when they call. A group of
sales representatives studied how to increase the number of customers who agree to
purchase the programs and found that many prospective customers believed it was
difficult to tell from the sample tape alone whether the educational programs would
meet their needs. The sales representatives performed an experiment to test whether
sending the complete-program tapes for review by customers would increase sales.
They selected 80 customers from the mailing list and randomly assigned 40 to receive
the full-program tapes for approval. They then recorded the number of tapes that were
purchased and returned in each group. The results of the study are shown at the top of
the next column.

TYPE OF VIDEOTAPE RECEIVED

ACTION

Sample

Full

Total

Purchased

Returned

Total

(a) At the 0.05 level of significance, is there evidence of a difference in the
proportion of tapes purchased on the basis of the type of tape sent to the
customer?
(b) On the basis of the results of (a), which tape do you think a representative
should send in the future? Explain the rationale for your decision.

To use Excel

Click Add-Ins| PHStat | Two-sample test | Chi-square tests for differences in proportions| (enter the required information)

Question 2 (25 Marks)

An increasing number of employees are exploring the Internet for savings in business
travel. An article (D. Rosato and S. Khan, “Net Surfing Nets Savings for Business
Travelers”, USA Today, March 7, 2000, 1B-2B) reported on the results of a survey of
400 corporate travel managers. Suppose that a contingency table of whether employees
researched airline ticket prices and booked airline tickets on the Internet revealed the
following results.

BOOKED AIRLINE TICKETS
ON THE INTERNET

RESEARCHED
AIRLINE TICKET
PRICES ON THE
INTERNET

Yes

Total

Yes

124

212

168

188

Total

108

292

400

(a) At the 0.05 level of significance, is there a significant relationship between
researching airline researching airline prices on the Internet and booking
airline tickets on the Internet?
(b) Determine the p-value in (a) and interpret its meaning.

To use Excel

Click Add-Ins| PHStat | Two-sample test | Chi-square tests for differences in proportions| (enter the required information)

Assignment 2 continued on next page!

Question 3 (20 Marks)

The sales representatives wanted to determine which initial approach would result in
more sales of the full-program tapes. Three approaches were to be studied: (1) a video
sales-information tape mailed to prospective customers, (2) a personal sales call to
prospective customers, and (3) a telephone call to prospective customers. A random
sample of 300 prospective customers was selected, and 100 were randomly assigned to
each of the three sales approaches. The results in terms of purchases of the full-program
tapes are as follows:

SALES APPROACH

ACTION

Videotape

Personal
Sales
Call

Telephone

Total

Purchase

Don’t
purchase

240

Total

100

300

(a) At the 0.05 level of significance, is there evidence of a difference in the
proportion of tapes purchased on the basis of the sales strategy used?
(b) Which sales approach do you think a representative should use in the future?
Explain the rationale for your decision.

To use Excel

Click Add-Ins| PHStat | Multiple-sample test | Chi-square tests for differences in proportions| (enter the required information)

Question 4 (30 Marks)

A consumer organization wanted to develop a model to predict gasoline mileage as measured
by miles per gallon based on the horsepower of the car’s engine and the weight of the car. A
sample of 50 recent car models was selected and the results are saved in AUTO.XLS (copy is
available in CD and blackboard).

(a) State the multiple regression equation
(b) Interpret the meaning of the slopes b1 and b2 in this problem
(c) Explain why the regression coefficients b0 has no practical meaning in this
example.
(d) Predict the average miles per gallon for cars that have 60 horsepower and
weighs 2,000 pounds.
(e) Determine the coefficient of multiple determination and interpret its meaning.
(f) At 0.05 level of significance, determine whether there is significant
relationship between miles per gallon and the two explanatory variables.

To use Excel

Organise your data set then Click Add-Ins| PHStat | Regression | Multiple Regression| (enter the required information)

Question 5 (for QM 262 Students Only! – 25 Marks)

Suppose the marketing department of a large supermarket chain wants to study the price
elasticity for packages of disposable razors. A sample of 15 stores with equivalent store traffic
and product placement (i.e., at the checkout counter) is selected. Five stores are randomly
assigned to each of three price levels (79, 99, and 119 cents) for the package of razors. The
number of packages sold over a full week and the price at each store are in the following
table: (DISPRAZ.xls)

Assume a quadratic relationship between price and sales.

(a) Set up a scatter diagram for price and sales.
(b) State the quadratic regression equation.
(c) Predict the average sales for a price of 79 cents.
(d) Determine whether there is a significant quadratic relationship between sales
and price at the 0.05 level of significance.
(e) At the 0.05 level of significance, determine whether the quadratic model is a
better fit than the linear model.
(f) Interpret the meaning of the coefficient of multiple determination.

To use Excel

Organise your data set (prepare the quadratic terms)

Click Add-Ins| PHStat | Regression | Multiple Regression| (enter the required information)

Assignment 3

Due Date: October 18, 2010

QM 162/262 (100 marks)

Weight: 10%

Question 1 (20 Marks)

The following data (in the file TREASURY.xls) represent the three-month Treasury
bill rates in the United States from 1991 to 2005. (The file treasury.xls is on the CD in
the back of the text book).

Year

Rate

Year

Rate

1991

5.38

1999

4.64

1992

3.43

2000

5.82

1993

3.00

2001

3.40

1994

4.25

2002

1.61

1995

5.49

2003

1.01

1996

5.01

2004

2.17

1997

5.06

2005

3.89

1998

4.78

Source: Board of Governors of the Federal Reserve System,

federalreserve.gov

(a) Plot the data.
(b) Fit a three-year moving average to the data and plot the results.
(c) Using a smoothing coefficient of W = 0.40, exponentially smooth the series and
plot the results.
(d) Repeat (c), using W = 0.15.
(e) Using results in (c) and (d), what is your exponentially smoothed forecast for
2006? Check the actual value for 2006.
(f) Compare the results of (c) and (d).

Question 2 (30 Marks)

The data in the file STRATEGIC.xls represent the amount of oil, in millions of barrels
held in the U.S. strategic oil reserve, from 1981 through 2004. (The file strategic.xls is
on the CD in the back of the text book).

Source: Energy Information Administration, U.S. Department of Energy, www.eia.doe.gov.

(a) Plot the data.
(b) Compute a linear trend forecasting equation and plot the trend line.
(c) Compute a quadratic trend forecasting equation and plot the results.
(d) Compute an exponential trend forecasting equation and plot the results.
(e) Which model is the most appropriate?

(f) Using the most appropriate model, forecast the number of barrels, in millions, for
2005.

Question 3 (20 Marks)

The shellfish catch and the wholesale prices in a coastal city for 2000 and for 2008 are
given in the following table (SHELLFISH.XLS).

Quantity (millions of kg)

Price per kg ($)

2000

2008

2000

2008

Clams

112

11.24

12.26

Crabs

335

301

11.09

12.28

Lobsters

11.73

12.63

Oysters

11.51

12.81

Scallops

11.65

12.69

Prawns

244

344

11.34

11.66

(a) By using 2000 as the base year, calculate the Paasche, Laspeyres and Fisher
price indexes.
(b) Interpret the results.

Question 4 (15 Marks)

Handy Home Centre specialises in building materials for home improvements. They
recently constructed an information booth in the centre of the store. Define X to be the
number of customers who arrive at the booth over a 5-minute period. Assume that the
conditions for a Poisson situation are satisfied with

λ=4 customers over a 5-minute period

(a) What is the probability that over any 5-minute interval, exactly four people
arrive at the information booth?
(b) What is the probability that more than one person will arrive?
(c) What is the probability that exactly six people arrive over a 10-minute period?

Question 5 (15 Marks)

J.D. Power and Associates calculates and publishes various statistics concerning car
quality. The initial quality score measures the number of problems per new car sold. For

2004 model cars, the Lexus had 0.78 problems per car. Assume that the number of
problems per new car is distributed as a Poisson random variable. What is the
probability that: {show your workings}

(a) a 2004 Lexus will have zero problems?
(b) a 2004 Lexus will have one or more problems?
(c) a 2004 Lexus will have two or less problems?

Marking policy

Plagiarism

You must comply with the University’s policy on Plagiarism and Academic
Misconduct. The next section in this booklet directs you to the policy, outlines your
responsibilities in connection with academic writing, and gives advice on how to avoid
plagiarism.

Assessment preview

Asking unit coordinators for preliminary review of any assessment tasks prior to formal
submission is inappropriate and unfair to other students without that opportunity.

Casual markers and moderation process

Students are advised that their assessment tasks may be marked by someone other than
a member of the teaching team. If this is the case, the Head of School will approve the
appointment of all casual markers, and the unit coordinator will moderate the marking
process to ensure competence, fairness and consistency.

Extensions and late submission

If you find that you cannot meet the published due date for an assignment, you must
contact the unit coordinator in writing no later than the due date to request an
extension. Any required supporting information, such as a medical certificate, should
be provided to the unit coordinator no later than the due date.

Extensions will be granted on the basis of unavoidable or unforeseen circumstances.
However, requests that relate to avoidable time management issues such as ‘heavy work
commitments in other units’ or ‘leaving my run a little late’ will not be considered
favourably.

Except under exceptional circumstances, the maximum possible extension that may be
requested is two weeks and only one extension is possible per assignment.

Assignments are deemed to be late if (i) they are not submitted (in accordance with the
submission requirements outlined above) on, or before, the published due date or (ii)

they are submitted after an assignment extension date that was previously negotiated
with the unit coordinator.

The penalties for late submission and for non-submission are as follows:

A compulsory assignment that is submitted late (or is not submitted) will result in the
grade NI (Failed Incomplete) for the unit.

A non-compulsory assignment that is submitted late (or is not submitted) will receive
0%.

Return of assessments

The unit coordinator will endeavour to have a student’s assignment marked and either
(i) available for collection by internal students, or (ii) returned to the Teaching and
Learning Centre within four (4) weeks of receiving the assignment. Please note, we will
return internal assignments only to their author; no student will be permitted to pick up
assignments for other students.

Of course, if you receive an assignment extension you can expect the return of your
work to be later than assignments submitted on time. This means that in some cases
assignments may not be returned before the next assignment is due or before the exam.

Re-marking of assessments tasks

Students may request that an assessment task be re-marked, in its original form, in
circumstances where the student presents a case arguing that the original marking was
unfair or inconsistent with marking guidelines. This request must be directly addressed
to the unit coordinator, with a copy to the Head of School, by the student within 10
working days of receipt of the original marked assessment task.

Assessment Information

Assessment policy

Information regarding all aspects of assessment can be found at
http://www.une.edu.au/secretariat/Academic-Board/policies/assessmentpolicy.pdf.

Information about special assessment (Special Examinations, Special Extension of
Time) can be found at http://www.une.edu.au/policies/alphabetic.htm#S.

Plagiarism

You must comply with the University's policy on Plagiarism and Academic Misconduct
(go to http://www.une.edu.au/policies/pdf/plagiarismcoursework.pdf for details). Your
work will be checked for originality.

Plagiarism is the action or practice of taking and using as one's own the thoughts or
writings of another without acknowledgment. The following practices constitute acts of
plagiarism and are a major infringement of UNE's academic values:

. where paragraphs, sentences, a single sentence or significant parts of a sentence
are copied directly, are not enclosed in quotation marks and appropriately
referenced;
. where direct quotations are not used, but are paraphrased or summarised, and the
source of the material is not referenced within the text of the paper; and
. where an idea which appears elsewhere in any form* is used or developed without
reference being made to the author or the source of that idea.

*Some examples of this are books, journals, WWW material, theses, computer stored
data and software, lecture notes or tapes.

Your responsibility

It is your responsibility to:

. read, understand and comply with the policy on Plagiarism and Academic
Misconduct found at the website above;
. familiarise yourself with the conventions of referencing for your discipline(s);
. avoid all acts which could be considered plagiarism or academic misconduct;
. seek assistance from appropriate sources if you become aware that you need more
knowledge and skills in relation to academic writing;
. be aware that when you submit an assignment through the University’s e-
Submission system, you are deemed to have signed the plagiarism declaration
form;
. submit a separate signed and dated plagiarism declaration form with every task,
report, dissertation or thesis submitted in hard copy for assessment or
examination.

Avoiding Plagiarism

You should refer to the following websites for further advice and assistance:

. Avoiding Plagiarism and Academic Misconduct (Coursework): Information for
Students http://www.une.edu.au/policies/pdf/plagiarismstudentinfocw.pdf.
This information explains the principles of good scholarship and has guidelines to
help you avoid plagiarism. It also has guidelines for referencing and research, and
advice on the use of internet sites.
. Academic Skills Office
http://www.une.edu.au/tlc/aso/students/publications/referencing.htm
The Academic Skills Office has a variety of support materials to assist you with
referencing and avoiding plagiarism.
. eSKILLS UNE Keeping Track
http://www.une.edu.au/library/eskillsune/keeping/index.htm
eSkills Keeping Track has advice about organising your information for
assignments and on referencing appropriately.

UNE grading system

Grade (Code)

Explanation

HD
High Distinction
85% and above

Excellent performance indicating complete and comprehensive
understanding and/or application of the subject matter; achieves all
basic and higher-order intended unit objectives and graduate attributes
linked to the assessment tasks; minimal or no errors of fact, omission
and/or application present; clear and unambiguous evidence of
possession of a very high level of required skills; demonstrated very
high level of interpretive and/or analytical ability and intellectual
initiative; very high level of competence.

D
Distinction
75 to 84%

Very good performance indicating reasonably complete and
comprehensive understanding and/or application of the subject matter;
achieves all basic and most higher-order unit objectives and graduate
attributes linked to the assessment tasks; some minor flaws; clear and
unambiguous evidence of possession of a high level of required skills;
demonstrated high level of interpretive and/or analytical ability and
intellectual initiative; high level of competence.

C
Credit
65 to 74%

Good performance indicating reasonable and well-rounded
understanding and/or application of the subject matter; achieves all
basic but only a few higher-order intended unit objectives and graduate
attributes linked to the tasks; a few more serious flaws or several minor
ones; clear and unambiguous evidence of possession of a reasonable
level of most required skills; demonstrated reasonable level of

interpretive and/or analytical ability and intellectual initiative;
reasonable level of competence.

P
Pass
50 to 64%

Satisfactory performance indicating adequate but incomplete or less
well-rounded understanding and/or application of the subject matter;
achieves many basic but very few or none of the higher-order intended
unit objectives and graduate attributes linked to the assessment tasks;
several serious flaws or many minor ones; clear and unambiguous
evidence of possession of an adequate level of an acceptable number of
required skills; demonstrated adequate level of interpretive and/or
analytical ability and intellectual initiative; adequate level of
competence.

N
Fail
Less than 50%

Unsatisfactory performance indicating inadequate and insufficient
understanding and/or application of the subject matter; achieves few or
none of the basic and higher-order intended unit objectives and
graduate attributes linked to the assessment tasks; numerous
substantive errors of fact, omission and/or application present; clear
and unambiguous evidence of non-possession of most or all required
skills; insufficiently demonstrated level of interpretive and/or analytical
ability and intellectual initiative; fails to address the specific criteria;
inadequate level of competence.

NI
Fail-Did not
satisfy unit
requirements

One or more mandatory requirements for the completion of the unit (as
detailed in the Unit Requirements) were not fulfilled.

S or US
Satisfactory or
Unsatisfactory

In some units, the grading system is organised on a
satisfactory/unsatisfactory (pass/fail) basis. When this grading system
is used the appropriate interpretive descriptors to apply will be those
for the grade of at least Pass or Fail.

W
Withdrawn

The student withdrew from the unit without academic penalty.

Examinations

The Examinations page at http://www.une.edu.au/exams/ has important information
about examinations, including your responsibilities as a student in relation to exams,
information about examination dates and special exams, and links to who to contact if
you have queries.

Appeals

Students wishing to lodge an appeal in relation to unit assessment; practical and/or
professional experience assessment; the application of faculty policies; Special
Examinations; and Special Extensions of Time, should consult the University's Student
Appeals Policy at: http://www.une.edu.au/policies/pdf/studentappealspolicy.pdf.

AskUNE

If you have questions related to assessment that are not covered in this booklet, go to
AskUNE. At AskUNE you can find answers to many common enquiries or submit an
enquiry of your own by clicking on the 'Contact Us' tab.

Tutorial Exercises

Tutorial 1

Review of Hypothesis Testing for Single Mean

Exercise 1.1

A manufacturer of television picture tubes has a production line that used to produce an
average of 100 tubes per day. Because of new government regulations, a new safety
advice are installed, which manufacturer believes will reduce daily output. After the
installation of the safety device, a random sample of 15 day’s production was recorded,
as follows:

Mean = 96.47 Sample Variance = 23.55 Sample Standard deviation: 4.85

Assuming that the daily output is normally distributed is there sufficient evidence to
allow the manufacturer to conclude that the average daily output has decreased
following the installation of the safety device. (Use α = 0.05).

Exercise 1.2

One scientific journal article claimed that the average use of pesticides in wheat
production in Narrawa is 5.9 litres per hectare. You are working for an Agro-Chemical
Company, so the value of the population mean is of vital interest to you. To investigate
the claims, you randomly selected 75 farmers and asked their pesticide use. Your results
for n = 75 are: Sample Mean = 5.76 litres and sample standard deviation = 0.48 litres.
At 5% level of significance, should we reject the claim that μ = 5.9?

Exercise 1.3

The owner of a local nightclub has recently surveyed a random sample of n = 250
customers of the club. She would now like to determine whether or not the mean age of
her customers is over 30. If so, she plans to alter the entertainment to appeal to an older
crowd. If not, no entertainment changes will be made.

(a) What are the appropriate hypotheses?
(b) Using 0.05 level of significance and the sample mean of 31.5 and sample standard
deviation of 4, should the owner proceed with the entertainment changes?

Relevant PHStat outputs are provided on next page.

t Test for Hypothesis of the Mean

Data

Null Hypothesis .

100

Level of Significance

0.05

Sample Size

Sample Mean

96.47

Sample Standard Deviation

4.85

Intermediate Calculations

Standard Error of the Mean

1.252264615

Degrees of Freedom

t Test Statistic

-2.818893033

Lower-Tail Test

Lower Critical Value

-1.76130925

p-Value

0.006831246

Z Test of Hypothesis for the Mean

Data

Null Hypothesis .=

Level of Significance

0.05

Population Standard Deviation

Sample Size

250

Sample Mean

31.5

Intermediate Calculations

Standard Error of the Mean

0.252982213

Z Test Statistic

5.929270613

Upper-Tail Test

Upper Critical Value

1.644853

p-Value

1.5266E-09

Ex. 1.2 Z Test of Hypothesis for the Mean

Data

Null Hypothesis .

5.9

Level of Significance

0.05

Population Standard
Deviation

0.48

Sample Size

Sample Mean

5.76

Intermediate Calculations

Standard Error of the Mean

0.055425626

Z Test Statistic

-2.525907428

Two-Tailed Test

Lower Critical Value

-1.959961082

Upper Critical Value

1.959961082

p-Value

0.011540028

Tutorial 2

Testing for Two Means

Exercise 2.1 (Two large independent samples)

Given a sample size of n1 = 40 from a population with known standard deviation (σ1 =
20), and an independent sample of size n1 = 50 from another population with known
standard deviation (σ2 = 10).

(a) What is the value of the test statistic for testing differences in two population
means if sample mean from population 1 is 72 and the sample mean from
population 2 is 66?

(b) What is your decision at 0.05 level of significance, if you are testing that there is
no significant difference between the two population means?

Exercise 2.2 (Two small independent samples)

The manufacturer of a small battery-powered CD Walkman decides to include 4
alkaline batteries with their product. Two battery suppliers are being considered; each
has its own brand, EveryGizer and EnergyReady. The supervising inspector of incoming
quality wants to know if the average lifetime is the same. Based on past experience, she
believes that the battery lifetimes follow a normal distribution. A simple experiment is
conducted, each of 10 batteries (5 of EveryGizer and 5 EnergyReady) that are
connected to a device that places a small drain on the battery power and records the
battery lifetime. The following results are obtained:

EveryGizer EnergyReady

n1=5 n2=5

Sample mean=44.2 Sample mean=31.6

Sample standard deviation=5.263 Sample standard deviation=4.159

Let μ1 be the average lifetime (if observed indefinitely) for EveryGizer, and μ2 be the
average for EnergyReady. We wish to determine whether the data allow us to conclude
that μ1 μ2, using α=0.05. USE PHStat to produce the computer output, see
instructions below.
≠

Notes: Testing the means of two samples

In order to address the issue of testing two samples, we use the same techniques already
introduced in QM 161 and in lectures of this unit, but apply them in new context. The
new information are summarised as follows:

. The two samples are drawn independently from normal populations.

. The notation used, n and for the sample
means; and s1 and n2 for the sample sizes,
1 and s2 are the standard deviations of the samples.
1X2X
. The sampling distribution of - is normal since the two original populations
are normal.
1X2X
. Remember from our previous work that the standard deviation for a single sample
from normal population is given by:

nσ

. When two samples are large, n- is given by
the expression:
1 and n2 > 30, and the standard deviation, σ is
known for the population (not equal), the standard deviation of 1X2X

222121nnσ+
σ

. When two samples are large, n- is estimated by the expression:
1 and n2 > 30, and the standard deviation, σ is not
known the standard deviation of 1X2X

222121nsns+

. When the samples are small, n 30, the standard deviation of -is
estimated by the expression:
1 and n2 ≤1X2X

where: ...
.
...
.
+
212pn1n1S2nns)1n(s)1n(S212222112p.+
.+.
=

Instructions: Using PHStat

. Double click PHStat

. Select PHStat|Two-Sample Tests| t Test for differences of two means

. In the t Test for Differences in Two means dialog box

- Enter the hypothesised value in the Hypothesized Difference: edit box (usually 0)

- Enter the value in the Level of Significance :edit box

- Enter the summary data for the two samples

- Select the test option (based on the format of your alternative hypothesis)

- Enter the title of your output, eg. QM 162: Tute 2

- Click OK button

Tutorial 3

Analysis of Variance and Kruskal-Wallis Test

Exercise 3.1

Consider the following data:

Aisle Location

Front

Middle

Rear

8.6

3.2

4.6

7.2

2.4

6.0

5.4

2.0

4.0

6.2

1.4

2.8

5.0

1.8

2.2

4.0

1.6

2.8

(a) Using PHStat, perform the Tukey-Kramer procedure in order to determine which
of the c means are significantly different?

(b) How many degrees of freedom are there in the numerator and denominator of the
Studentized range distribution?

(d) What is the value of the critical range?

Exercise 3.2

Given a two-factorial design having three levels in factor A, three levels in factor B, and
four replicates in each of the nine treatment cell combinations of factors A and B,
complete the following ANOVA summary table.

Source

Degrees of
freedom

Sum of
Squares

Mean Square

Sample

r-1

SSFA

120

MSFA=SSFA/r-1

F=MSFA/MSE

Columns

c-1

SSFB

110

MSFB=SSFB/c-1

F=MSFB/MSE

Interaction

(r-1) (c-1)

SSAB ?

MSAB=SSAB/(r-
1)(c-1)

F=MSAB/MSE

Within

rc(n’-1)

SSE

270

MSE=SSE/rc(n’-1)

Total

n-1

SST

540

(a) At 0.05 level of significance, what is the upper-tailed critical value from the F
distribution for the factor A, factor B and interaction effect, respectively?

(b) What is your statistical decision with respect to interaction effect?

(d) What is your statistical decision with respect to factor B?

Exercise 3.3

The manager of a supermarket chain wanted to study the effects of product location on
the sales of packages of candy bars. Two factors were to be studied, location in aisle
either front, middle or rear; and shelf-location, either top or bottom. A random sample
of 12 equal sized stores was selected and two stores were randomly assigned to each
combination of aisle location and shelf location. The size of the display area was the
same in all stores. At the end of one-week trial period, the sales of packages of candy
bars in each store are as follows:

Shelf

Aisle location

Front

Middle

Rear

Top

Bottom

(a) At the 0.05 level of significance:

(i) Is there an interaction effect between aisle location and shelf location?

(ii) Is there a difference between aisle locations?

(iii) Is there a difference between shelf locations?

(b) Plot a graph of the average sales for each aisle location for each shelf location.

Exercise 3.4

A manufacturer of high-quality calculators is trying to decide which one of the three
types of battery to include with each calculator sold. The two key determinants of the
decision is the cost and the length of life of the battery. In order to assess the latter
factor, 5 calculators were equipped with TYPE 1 batteries; another 5 calculators were
equipped with TYPE 2 batteries, and yet another 5 calculators were equipped with
TYPE 3 batteries. The 15 calculators were run until the batteries wore out. The times
until the battery wear-out were recorded and are shown on the following table.

TYPE 1 TYPE 2 TYPE 3

15.5 20.5 13.3

17.2 18.3 18.9

13.3 21.2 19.5

20.6 15.7 15.2

19.2 16.3 13.8

(a) At the 5% level of significance, is there a difference in the length of life of the
three batteries?

(b) Which type of battery would you think be used in the manufacturing of the
calculators?

Notes: Two-Way Analysis of Variance

Two-way ANOVA is used to analyse the effect of two-factors on a given dependent
variable. The two factors may differ with respect to the number of levels or groups they
contain. ANOVA is used to analyse differences among group means, using the
information on the variation in factor A, factor B, interaction and within (random
variation).

Notations used:

SST: Total Variation (Total Sum of Squares) (df=n-1)

SSFA: Factor A variation (df=r-1)

SSFB: Factor B variation (df=c-1)

SSAB: Interaction variation (df=(r-1)(c-1))

SSE: Random variation (df=rc(n’-1))

MSFA: Mean Squares associated with Factor A

MSFB: Mean Squares associated with Factor B

MSAB: Mean Squares associated with interaction effect

MSE: Mean Squares error

n: the number of observations

r: the number of rows

c: the number of columns

n’: the number of values (replications) for each cell.

d.f: Degrees of freedom

F: F-test statistic

Fu: Upper critical value

How to obtain the critical value?

To test for Factor A: Fα,(r-1),(rc(n’-1)

To test for Factor B: Fα,(c-1),(rc(n’-1)

To test for interaction effect: Fα,(r-1)(c-1),(rc(n’-1)

Instructions (Using Excel)

. Enter the data in excel. The first row should be the variable name or label.

. Select Tools | Data Analysis

. Select Anova: Two-factor with replication from the Analysis Tools list box in the
Data Analysis dialog box. Click the OK button.

. In the Anova: Two- Factor with replication dialog box:

. Enter the data range in the input range edit box.

. Enter the number of rows per sample.

. Enter 0.05 in the Alpha edit box

. Select the New Worksheet Ply option button and enter a name for the new sheet.

. Click the OK button.

How to plot the graph?

(a) Obtain the average values in each combinations

(b) Enter the data in a separate worksheet.

Notes: Kruskal-Wallis

. We want to test if theirs is significant difference in the location of the population.

. H0: All c populations have the same median values

. H1: Not all medians are the same.

. Pool the data from lowest to highest.

. Assign ranks from lowest to highest (1 for lowest and n for highest, average ranks
in case of ties).

. Calculate the sum of ranks for each group.

. Compute the test statistic

21123(1)
(1)
ciiiTHnnnn=
..
=.+..+..
Σ

. Reject Ho if H > χ2c-1.

Instructions (PHStat)

Select PHStat | c-sample tests | Kruskal-Wallis Rank Test

{Complete the dialog box, all of them are self-explanatory)

Please note: PHStat does not work properly if the c-sample sizes are not equal. In this
case, you need to compute the value of the test statistic manually.

Tutorial 4

Kruskal-Wallis and Testing for Proportions

Exercise 4.1

TYPE 1

TYPE 2

TYPE 3

15.5

20.5

13.3

17.2

18.3

18.9

13.3

21.2

19.5

20.6

15.7

15.2

19.2

16.3

13.8

(a) At the 5% level of significance, is there a difference in the length of life of the
three batteries?

(b) Which type of battery would you think be used in the manufacturing of the
calculators?

Exercise 4.2: Testing for Differences of 2
Population Proportions

Of a random sample of 100 rebuilt engines from Engine Masters (Population 1), 28
failed with-in the 12-month warranty period. A second sample, obtained independent of
the first, consisted of 150 engines rebuilt by Excel Motors (population 2), 48 of which
failed during the 12-month warranty period. Both sets of engines were subjected to the
same weather conditions, engine stress, and maintenance program. Determine whether
there is any difference between the proportion of Engine Masters engines and the
proportion of Excel Motors engines that failed in the one-year warranty period.

(a) At 5% level of significance, is there evidence to support that a significant
difference between the proportion of Engine Masters engines and the proportion
of Excel Motors engines that failed in the one-year warranty period? Use Z-test.

(b) Use chi-square to test the hypothesis in (1). Need to produce the output first.

The following is the contingency table for the above problem.

Engine Masters

Excel Motors

Total

Failed

Did not fail

102

174

Total

100

150

250

Notes and PHStat Instructions

Notes: Kruskal-Wallis

. We want to test if theirs is significant difference in the location of the population.

. H0: All c populations have the same median values

. H1: Not all medians are the same.

. Pool the data from lowest to highest.

. Assign ranks from lowest to highest (1 for lowest and n for highest, average ranks
in case of ties).

. Calculate the sum of ranks for each group.

. Compute the test statistic

21123(1)
(1)
ciiiTHnnnn=
..
=.+..+..
Σ

. Reject Ho if H > χ2c-1.

Instructions (PHStat)

Select PHStat | c-sample tests | Kruskal-Wallis Rank Test

{Complete the dialog box, all of them are self-explanatory)

Please note: PHStat does not work properly if the c-sample sizes are not equal. In this
case, you need to compute the value of the test statistic manually.

Testing for Two Proportions

. PHStat | Two-Sample Tests | Chi-square Test for Differences in Two Proportions
. Enter the appropriate level of significance
. Type in the title of your output
. An empty worksheet will be produced – you need to enter the data in the
“observed frequencies table”.
. The remaining values will be calculated for you!

Testing for More than Two Proportions

. PHStat | Multiple-Sample Tests | Chi-square Test

. Enter the appropriate level of significance, number of rows and number of
columns
. Type in the title of your output
. An empty worksheet will be produced – you need to enter the data in the
“observed frequencies table”.
. The remaining values will be calculated for you!

Tutorial 5

Testing for Differences in Population Proportions

Exercise 5.1: Testing for Differences of more
than 2 Population Proportions

The marketing director of a cable television company is interested in determining
whether there is a difference in the proportion of the households that adopt a cable
television service based on the type of residence (single-family dwelling, two-to-four
family dwelling, and apartment house). A random sample of 400 households revealed
the following:

Purchase cable
television

Type of residence

Total

Single-family

Two-to-four
family

Apartment
house

Yes

210

190

Total

150

175

400

(a) At the 0.05 level of significance, is there evidence of a significant difference
among types of residence with respect to the proportion of households that adopt
the cable TV service?

Testing for Two Proportions

Exercise 5.2

A record company wanted to survey its customers regarding music preferences. A
random sample of 258 frequent customers of the record company was selected, and
information was gathered on their music preference and job classification. From the
following data, is there sufficient evidence of a significant relationship between type of
music preferred and working? Use 5% significance level?

Job
Classification

Country and
Western

Rock

Classical

Jazz

Total

Clerical

Managerial

Blue Collar

Total

258

Testing for More than Two Proportions

. PHStat | Multiple-Sample Tests | Chi-square Test
. Enter the appropriate level of significance, number of rows and number of
columns
. Type in the title of your output
. An empty worksheet will be produced – you need to enter the data in the
“observed frequencies table”.
. The remaining values will be calculated for you!

Tutorial 6

Testing for Independence, Equality of Variances and Wilcoxon Rank Test

Exercise 6.1

A public official working on health reform policy wants to compare occupancy rates
(i.e., average annual percentage of beds filled) in urban versus sub-urban hospitals
within his state. A random sample of 16 urban hospitals and a random sample of 16
suburban hospitals are selected within the state and the occupancy rates are recorded as
follows:

Urban
Hospital

76.5

75.9

79.6

77.5

79.4

78.7

78.6

79.3

73.3

77.4

79.9

70.4

77.7

78.1

75.9

Rural
Hospital

71.5

73.4

74.6

74.3

71.2

67.8

76.9

75.5

70.7

67.4

62.6

76.5

At 5% level of significance, is there evidence of a difference in the variances in
occupancy rates between urban and suburban hospitals in the state?

PHStat Instructions

Testing for Independence

1. Select PHStat| Multiple-sample test | chi-square test
2. Enter the level of significance
3. Enter the number of rows
4. Enter the number of columns
5. Type in a title for the worksheet
6. Then click OK.
7. Enter the data in the observed frequency table (the data are obtainable from the
contingency table provided).
8. If the value of the chi-square test statistic is not produced, you have to compute
them manually using the values in the expected frequency table. Use the chi-
square formula.

The format:

Let X and Y are the two factors to be analysed.

The hypotheses:

H0: X and Y variables are independent (there is NO relationship between X and Y)

H1: X and Y variables are not independent

The test statistic: 22()oeefff.
χ=Σ

(The value of the test statistic should be taken from the PHStat output OR be
computed manually!)

The critical value and decision rule: Critical value: χ2(α) (r-1)(c-1). Reject H0 if
χ2>χ2(α) (r-1)(c-1), otherwise do not reject H0

The decision and conclusion: This must be consistent with the decision rule and
must answer the question in the problem, ie. must be consistent with the claim.

Testing for Equality of Variances

1. Select PHStat | Two-sample test | F-test for differences in variances
2. Enter the level of significance.
3. Enter the standard deviation and sample size of each population.
4. Select the appropriate test options.
5. Type a title for the output.
6. Then click OK.

The format:

Let X and Y are the two factors to be analysed.

The hypotheses:

H0: σ21 = σ22 σ21 >= σ22 σ21 =< σ22

H1: σ21 ≠ σ22 σ21 < σ22 σ21 > σ22

The test statistic: (The value of the test statistic should be taken from the
PHStat output OR be computed manually!)
2122SFS=

The critical value and decision rule:

Critical value: Upper-critical value : FU = Fα, n1-1, n2-1: Lower critical value: FL = 1/ Fα,
n2-1, n1-1

Reject H0 if F > Fu or if F < FL, otherwise do not reject H0.

The decision and conclusion: This must be consistent with the decision rule and
must answer the question in the problem, ie. must be consistent with the claim.

Exercise 6.2: Small Sample Test

The Road Travel Authority would like to compare the scores of those who sit for the
Driver Knowledge Test (DKT). They would like to find out if there is a difference in
the scores of those who just read the Road User’s Handbook, and those read and
practice the questions in the Internet. Prior to sitting the examination, the examinees
were asked to specify the nature of their preparation. The examiner randomly selected a
sample of 4 for those who just read the handbook and a sample of 6 for those who
practice the questions in the Internet and their scores were recorded as follows:

Read Road User’s
Handbook

Practice in the Internet

Is there evidence to believe that there is significant difference in the median scores of
between the two groups of examinees? Use α = 0.05.

{Outline the decision rule for the above problem if we have a lower and an upper tailed tests}.

Exercise 6.3: Large Sample Test

Urban
Hospital

76.5

75.9

79.6

77.5

79.4

78.7

78.6

79.3

73.3

77.4

79.9

70.4

77.7

78.1

75.9

Rural
Hospital

71.5

73.4

74.6

74.3

71.2

67.8

76.9

75.5

70.7

67.4

62.6

76.5

(a) At 5% level of significance, is there evidence of a difference in the median in
occupancy rates between urban and suburban hospitals in the state?

Small samples

. Pool data

. Assign ranks

. Obtain sum of ranks (T1 for group 1 and T2 for group 2)

. Use T1 as test statistic

. Obtain critical value from Table E.6

. Perform the test.

Large samples

. Pool data

. Assign ranks

. Obtain sum of ranks (T1 for group 1 and T2 for group 2)

. Compute the mean of T1 ()
2)1n(n11T+
=μ

. Compute the standard deviation of T1 ()
12)1n(nn211T+
=σ

. Compute the value of the test statistic ()
tT1T1TZσμ.
=

. Obtain critical value from Table E.2a

. Perform the test.

Tutorial 7

Regression Analysis

Exercise 7.1

An agriculture student from the University of New England pulled from his father’s
farm records some data relating to crop yield to amount of fertilizer used, mean seasonal
rainfall, mean number of hours of sunshine and mean daily temperature. As a first
approximation, he wishes to regress crop yield on amount of fertilizer used, based on
the data provided in the following table.

Fertilizer
(kg/hectare)

Crop Yield ('000
kg/hectare)

220

450

250

320

500

250

330

430

240

280

370

400

420

450

(a) Graph the data and comment on the suitability of using a linear regression model.

(b) State and report the regression model.

(d) Report and interpret the coefficient of determination.

(e) Forecast crop yield if farmer will apply 475 kg of fertilizer.

Exercise 7.2

A large consumer product company wants to measure the effectiveness of different
types of advertising media in the promotion of its products. There are three types of
advertising media considered: radio advertising, TV advertising, and newspaper
advertising. A sample of 22 cities with approximately equal populations is selected for
study during a test period of one month. Each city is allocated a specific expenditure
level for all the advertising media. The sales of the product (in thousands of dollars) and
also the levels of media expenditure during the test month are recorded.

Sales

Radio

Newspaper

Sales

Radio

Newspaper

973

1577

1119

1044

875

914

625

1329

910

1330

971

1405

931

1436

1177

1521

882

1741

982

1866

1628

1717

Use PHStat to run the multiple regressions:

Using the PHStat output, answer the following questions:

(a) State the multiple regression equation.

(b) Interpret the meaning of the coefficients in the equation.

(c) Predict the average sales if the advertising expenditures for radio, TV and
newspaper are $5,000, $30,000 and $20,000, respectively.

(d) Interpret the meaning of the coefficient of multiple determination.

(e) At the 0.05 level of significance:

(f) Determine whether there is significant relationship between the sales of product
and the three explanatory variables.

(g) Determine whether each explanatory variable makes a significant contribution to
the model.

(h) On the basis of the results, state the appropriate regression model for this problem.

(i) Set up 95% confidence interval estimate for the true population slope between
sales and TV advertisement.

(j) Determine the adjusted R2 and interpret its meaning.

Tutorial 8

Dummy Variables

The production manager of a company that manufactures car seats has been concerned
about the number and cost of machine breakdowns. The problem is that the machines
are old and becoming quite unreliable. However, the cost of replacing them is quite
high, and the manager is not certain that the cost can be made up in today’s slow
economy. To help make a decision about replacement, he gathers data about last
months, costs for repairs and the ages (in months) of the plant’s 20 machines. The data
are as follows:

Repairs

Age

Machine

327.67

110

376.68

113

392.52

114

443.14

134

342.62

476.16

141

324.74

115

338.98

115

433.45

115

526.37

142

321.86

127

303.73

164

301.06

159

279.24

155

327.94

179

281.74

146

393.35

134

265.16

150

350.30

159

123.88

121

Repairs: cost of repairs

Age: age of machine

Machine: Type of machine (1: welding machine; 0; other machine)

(a) Develop a multiple regression model.

(b) Interpret the coefficients.

Tutorial 9

Exponential Smoothing and Forecasting

Exercise 9.1

The annual demand for energy in the Austbourne is affected by various factors,
including price, availability and the state of the economy. To help analyse the changes
that have taken place and to develop prediction, the annual total consumption of energy
in Austbourne was recorded from 1980-96.

Year

Time Period t

AEC (Yt)

1980

66.4

1981

69.7

1982

72.2

1983

74.3

1984

72.5

1985

70.6

1986

74.4

1987

76.3

1988

78.1

1989

78.9

1990

1991

1992

70.8

1993

70.5

1994

74.1

1995

1996

73.9

1. Plot the data on the chart.
2. Using a smoothing coefficient of W = 0.3
a. Exponentially smooth the series and plot the results in your chart.
b. What is the forecast for 1997?

3. Using a smoothing coefficient of W = 0.7
a. Exponentially smooth the series and plot the results in your chart.
b. What is the forecast for 1997?

BOX 1: How to use excel to generate the plot

Enter the data in Excel

Choose Insert | Chart

From the standard chart types, choose Line

From the chart-subtype, choose the 2nd on the first column

Click Next, click Series, click Add

Type the Name of the series (eg. AEC(Yt))

Click Values, and highlight the series of the Y-values

Click Category X-axis labels and highlight the X-values (eg. year column)

Click Next, type in the necessary titles of the chart, x-axis and y-axis

Click Next, click As object in Sheet #, then Finish

BOX 3: How to perform exponential smoothing: Using Excel

{Use W=0.3}

Open the file

Choose Tools | Data Analysis | Exponential Smoothing

In the Exponential Smoothing dialog box:

Type or highlight the series and enter on the Input range text box

Type 0.7 in the damping factor {Damping factor = 1-W}

Select the labels check box

Select the output range {where to put the exponentially smoothed series, eg.
D1:D18)

Click OK

Replace # N/A that appears in D1 with ES(0.3)

Select cell D17, position the cursor in the lower right corner and drag it down to D18 to
calculate for the value in that last cell.

Repeat the process for W=0.7 and save the series in column E

BOX 2: How to perform exponential smoothing: Manual computation

Et = WYt+(1-W)Et-1

Et = Exponentially smoothed series

W = assigned weight (0<W<1)

Yt= periods actual value

Et-1 = last period’s smoothed value

Example: Use W=0.3

Type a label in your column D (eg. ES(0.3))

For your first period, you have: E1 = Y1 = 66.4

E2 = (0.3) x (69.7) + (0.7)*66.4 = 67.4

E3 = (0.3) x (72.2) + (0.7)*67.4 = 68.8

BOX 4: How to add the smooth-series data in the chart

Click inside the original chart

Right click your mouse, select Source Data| Click Series | Add | and proceed with the
steps outlined in box 1 above.

BOX 5: How to forecast?

{When exponential smoothing is used for forecasting, next period’s
forecast is given by the last period’s smoothed value}
T1TEY.=+

Tutorial 10

Moving Averages and Trend Fitting

Exercise 10.1

Quarterly sales of a department store chain were recorded for the past four years. These
figures are shown below:

Year

Quarter

Sales ($ million)

1999

2000

2001

2002

(a) Calculate the 4-point centred moving averages and seasonal indexes under the
additive series assumption.

(b) Using the linear trend defined as: Yt = 24.95 + 0.89 t, and the computed seasonal
indexes, forecast the expected sales in the next four quarters of 2003.

Exercise 10.2

(a) Fit linear and quadratic trend models and forecast the consumption in 2003-2006.

Assessment

AECyearTP(Yt)
1986166.41987269.71988372.21989474.31990572.51991670.61992774.41993876.31994978.119951078.9199611761997127419981370.819991470.50001574.12001167420021773.9

QM162/262 Business Statistics 2

Tutorial 11

Index Numbers and Miscellaneous Distributions

Exercise 11.1: Index Numbers

The following table reflects the typical family’s buying habits per 6 months on repairs
for the family car. Use 2001 as the base year.

Item

2000

Price

2000

Quantity

2001

Price

2001

Quantity

2002

Price

2002

Quantity

Lube job

3.50

5.00

8.00

Oil
change

9.50

13.00

15.00

Tune-up

29.95

39.95

45.35

New
Tires

35.95

49.00

56.00

(a) Construct the Laspeyres index for 2000 and 2002.

(b) Construct the Paasche index for 2000 and 2002.

(d) Interpret the results in (1) to (3).

Tutorial 12

Poisson and Exponential Distribution

Exercise 12.1: Poisson Distribution

The auto parts department of an automotive dealership sends out an average of six
special orders daily. The number of special orders is assumed to follow a Poisson
distribution.

(a) What is the probability that for any day, the number of special orders sent out will
be exactly 2?

(b) What is the probability that for any day, the number of special orders sent out will
be more than 2?

Exercise 12.2: Exponential Distribution

Telephone calls arrive at the information desk of a large computer software company at
a rate of 15 per hour.

(a) What is the probability that the next call arrives within 3 minutes?

(b) What is the probability that the next call arrives within 20 minutes

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