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STA2020F Final Exam 2006

# STA2020F Final Exam 2006 - UNIVERSITY OF CAPE TOWN...

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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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f) 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 Q-statistic 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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STA2020F Final Exam 2006 - UNIVERSITY OF CAPE TOWN...

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