Exam (elaborations)
Sta exam past paper and memo
- Course
- Sta3022F (STA3022)
- Institution
- University Of Cape Town (UCT)
2013 paper with memo
[Show more]
Seller
Follow
Content preview
UNIVERSITY OF CAPE TOWNDEPARTMENT OF STATISTICAL SCIENCES
STA3022F
JUNE 2013 EXAMINATION
INTERNAL EXAMINERS: A/Prof S Lubbe, Dr Ş Er TOTAL MARKS: 100
INTERNAL ASSESSOR: A/Prof F Little
EXTERNAL EXAMINER: Dr T Berning TIME ALLOWED: 3 hours
PAGES: 14
INSTRUCTIONS: ANSWER EACH SECTION IN A SEPARATE BOOK.
ALL QUESTIONS MAY BE ATTEMPTED.
MARKS ARE ALLOCATED FOR INTERMEDIATE CALCULATIONS.
SECTION A: EXPLORATORY METHODS [Available marks: 51]
Question 1 [3 marks]
Consider a data set of the monthly inflation rate over several years for all African countries.
(a) Would you consider inflation rate to be a numerical, ordinal categorical or nominal variable.numerical(1)
(b) If the inflation figure for Zimbabwe for June 2012 is missing, name one method of overcoming this
problem.impute withmean (1)
(c) You want to perform an analysis that requires normally distributed data. You plotted histograms of the
data, some of which are shown below. Since the data is very skew, what can be done before embarking
on the analysis? transform the data with log transformation (1)
300
400
250
150
300
200
Frequency
Frequency
Frequency
100
150
200
100
100
50
50
0
0
0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.0 0.2 0.4 0.6 0.8 0.0 0.1 0.2 0.3 0.4
x x x
200
250
150
150
200
Frequency
Frequency
Frequency
150
100
100
100
50
50
50
0
0
0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.0 0.1 0.2 0.3 0.4 0.5
x x x
1
, Question 2 [15 marks]
Consider the following contingency table and associated R output. In the table below, 300 people
were asked what bank they used most often and to identify the most important reason why they
chose that bank.
Helpful Enjoy Branch close Keeps me Many Competitive
TOTAL
staff advertising to home informed ATMs interest rates
É FNB
ABSA
14
13
14
6
2
10
23
15
7
5
12
21
72
70
NEDBANK 11 16 8 4 10 8 57
STDBANK 12 14 30 8 28 9 101
TOTAL 50 50 50 50 50 50 300
> ca(bank.data)
Principal inertias (eigenvalues): iii
1 2 3
Value 0.174676 0.046073 0.021778 i
IE Percentage 72.02%
Rows:
FNB ABSA
19%
NEDBANK
8.98%
STDBANK
iiiiiiiiii
Mass 0.240000 0.233333 0.190000 0.336667
ChiDist 0.542201 0.468606 0.383164 0.525126
Inertia 0.070556 0.051238 0.027895 0.092838
Dim. 1 -1.172400 -0.794016 0.278962 1.228645
Dim. 2 -0.781987 1.457919 -1.315956 0.289685
ÉTÉ Columns:
Branch Competitive
Helpful Enjoy close Keeps me Many interest
staff advertising to home informed ATMs rates
Mass 0.166667 0.166667 0.166667 0.166667 0.166667 0.166667
ChiDist 0.205443 0.400249 0.618174 0.614089 0.516271 0.476418
Inertia 0.007034 0.026700 0.063690 0.062851 0.044423 0.037829
Dim. 1 -0.427021 0.023291 1.378472 -1.336570 1.197046 -0.835218
Dim. 2 -0.278986 -1.788994 1.041542 0.087283 -0.301211 1.240367
2 (a) In order to test the hypothesis 𝐻 : no significant association between bank and reason for using that
bank, give the test statistic and its associated distribution. Also define each of the symbols you use in the
definition of the test statistic and indicate how to calculate or obtain them. (4)
EE n in mm I Effffitate for Iii Eckart EYrtw9 andgrand
EE
umn
(b) Give an expression for the Pearson residuals calculated for a contingency table.
tff.gg (1)
(c) Once the matrix of Pearson residuals is obtained, each entry is divided by the grand total from the
contingency table. Name and give a mathematical expression for the method of obtaining the CA map
coordinates from this matrix.
supsingularvaluedecomposition Si Ar EE (2)
UiaVin
(d) Construct a CA map for the contingency table above. (5)
(e) What proportion of variance in the data are you displaying in your map in (d)?72.02719 91.021 (1)
(f) Which bank provides the most competitive interest rates? (1)
ABSA
(g) Why do customers tend to choose Nedbank? (1)
Enjoy advertising
2
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through EFT, credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying this summary from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller hslisa001. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy this summary for R89,33. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
67474 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy summaries for 14 years now