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UNIVERSITY OF CAPE TOWN
DEPARTMENT OF STATISTICAL SCIENCES
UNIVERSITY EXAMINATION JUNE 2006
STA2020F
Internal examiners:
Dr J. Nyirenda
Time: 3 hours
Mr K. Stielau
Full Marks = 100
Mr C. Holdsworth
Mrs H. Short
External examiner:
Prof. P. Fatti
Total no. of pages:
28
Instructions
: Answer section A in your blue answer book and section B on the red
multiple choice answer sheet. Negative marking in effect for multiple choice section. The
relevant statistical tables are provided at the end of this exam paper.
SECTION A – WRITTEN QUESTIONS
[60 Marks]
Question 1:
The South African Revenue Service (SARS) is always looking for ways to improve
the wording and format of its tax return forms. Three new forms have been developed
recently. To determine which, if any, are superior to the current form, 120 individuals
were asked to participate in an experiment. Each of the three new forms and the
currently used form, therefore four forms in total, were filled out by 30 different
people. 10 taxpayers in each group of 30 people are in the low income bracket, 10 are
in the next income bracket, and the remaining 10 are in the high income bracket. The
amount of time (in minutes) taken by each person to complete the task was recorded,
and each taxpayer only filled in one form.
SARS wishes to determine whether there
is a difference in the time taken to complete the income tax return form depending on
the type of form being completed and the income group that the taxpayer falls into.
The partially completed ANOVA table for this experiment is given below.
(Use a 5%
level of significance for all tests).
Source of Variation
SS
df
MS
F
F crit
Sample
6718.72
2
3359.36
e
3.07
Columns
b
a
2093.29 2.56
2.68
Interaction
5101.88
6
d
1.04
f
Within
c
108
816.82
Total
106317.47 119
a)
Fill in the missing values labelled a to f.
(6)
b) What is the response variable in this experiment?
(1)
c)
State, in words, the null and alternate hypotheses being tested in the test for
interaction.
(1)
d) Is interaction present between the variables in this experiment? (
Give a
reason for your answer and refer to your hypotheses given above.
)
(2)
e)
State, in words, the null and alternate hypotheses for the test of differences in
time taken to complete the income tax forms given different income groups.(1)
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Is there a difference in time taken to complete the income tax forms given
different income groups? (
Give a reason for your answer and refer to your
hypotheses given above.
)
(2)
[13]
Question 2
:
a) Which steps would one need to perform in order to forecast a time series using
AR modelling?
(6)
b) The residuals after fitting an AR(3) to a time series with 70 observations gives
a Qstatistic of 8.95 at lag 12 . Test whether the residuals from the above
AR(3) model are random up until lag 12.
(4)
c)
Discuss the source of each one of the four components of a time series in
financial (specifically value of sales) data.
(4)
d) When should one use MAD as aside from MSE to measure forecast accuracy?
(1)
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 Spring '11
 

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