University of Cape Town – Department of Statistical Sciences
STA2020F Exam June 2023
Examiners: Ms. Kelly Williams Marks: 100
Ms. Heiletjé van Zyl
Mr. Neil Watson Internal Examiner: Mr. Stefan Britz
External examiner: Prof G.D Sharp
Instructions:
• You have 3 hours to complete this exam.
• Answer ALL questions.
• Marks are awarded for intermediate calculations.
• Round all answers to 2 decimal places unless otherwise specified. DO NOT round intermediary
calculations.
• Answer Section A on the MCQ sheet provided; Sections B in a separate answer book, Section C in a
separate answer book and then Section D and Section E in one answer book. You should hand in 3
answer books in total.
• Start section E on a NEW page in your third answer book.
• For all MCQ questions, select the MOST correct answer.
Section A: MCQ [34]
Question 1 (2)
Which of the following is NOT a one-way ANOVA assumption ?
A) Observations are approximately normally distributed.
OB) Each treatment level has the same number of replicates.
C) Observations come from a distribution with equal population variances.
D) Observations are independent of one another.
E) C and D
Question 2 (2)
Which of the following IS a type of experimental design ? ANOVA
A) A completely randomised design RD one way
two ANOVA
B) A blocking ANOVA
C) A two-way design Read wayANOVA
two
D) A and C factorial way
E) A, B and C x
Design with interaction
Question 3 (2)
Factor A and Factor B are said to interact if:
A) Factor A is independent of Factor B.
B) Factor B has a different effect on the response variable depending on the level of Factor A.
C) The level of Factor A changes for different levels of Factor B.
D) Factor A has a different effect on the response variable depending on the level of Factor B.
E) B and D
Page 1
, Stat SStrt t SSresid
Question 4
SStot SStr t t SSblock SSresid
(2)
Adding a blocking variable to a completely randomised design will always have the following effect on the results
of an ANOVA:
O
A) Reduce the residual variation. V ft 9
B) Reduce the F-statistic of the treatment variable.
x
C) Increase the number of experimental units required.
D) Reduce the F-statistic of the blocking variable.
Insite
E) Increase the number of replicates in the experiment.
variable inCR
no
blocking
qÉÉÉ
Question 5
Multiple linear regression analysis is applicable when:
(2)
A) All of the independent variables are continuous.
B) The dependent variable is binary, whilst the independent variables are continuous only.
C) The dependent variable is continuous, and there is only one independent variable.
D) The dependent variable is continuous, and there are many independent variables which are either
continuous or categorical in nature.
E) The dependent variable is continuous, and there are many independent variables which are only
continuous in nature.
Question 6 (2)
A person, who has been vaccinated for malaria, recently visited Nigeria. After reporting this to a doctor at a regular
check-up appointment, the doctor still insisted on performing a malaria rapid diagnostic test. The test result came
out to be positive, even though the person actually does not have malaria. This is an example of:
A) A positive predicted value
B) A false negative
C) A false positive
D) A negative predicted value
E) None of the above
Question 7 (2)
If the coefficient of determination is 0.7510, what is the correlation coefficient value?
A) 75.10%
Tio
B) 56.40%
0C) 86.66%
D) 50.00%
866602
E) There is not enough information to calculate this value. 0
Question 8 (2)
Given the below confusion matrix and assuming disease (coded as 1) is the outcome of interest, compute the
positive predictive value (PPV) and negative predictive value (NPV).
OBSERVED
Disease No disease
ppr s
Disease 107 25
8 89
PREDICTED
a
NPV
No disease
Female 13 89
c d
Page 2
, A) PPV = 89.17% and NPV = 78.07%
B) PPV = 81.06% and NPV = 78.07%
C) PPV = 78.07% and NPV = 89.17%
D) PPV = 87.25% and NPV = 81.06%
E) PPV = 81.06% and NPV = 87.25%
Study the output of an exponential smoothing model below and then answer Questions 9 to 11.
A o 5611 18820 t
1 0.56117 19.568910.4046
19.76
0.3454 21.7005 21,3394 t
1 0.34547 0.4030
0.3885
0.0002 5.4748 t
1 00002 0.9020
0 9020
D 292412 3 0.8007
XO 9882
31.2 699
Question 9 (2)
If you were to apply moving average smoothing with a value of k = 3 to the original time series data, what would
be the first and third smoothed values?
A) 58.42; 76.17
1768 206
11 20
B) 19.47; 20.77 1st 19.47
C) 17.68; 25.38
20.14 22
D)
E)
19.47; 25.39
A; 20.46 3rd 19.31
39 20.77
Page 3
STA2020F Exam June 2023
Examiners: Ms. Kelly Williams Marks: 100
Ms. Heiletjé van Zyl
Mr. Neil Watson Internal Examiner: Mr. Stefan Britz
External examiner: Prof G.D Sharp
Instructions:
• You have 3 hours to complete this exam.
• Answer ALL questions.
• Marks are awarded for intermediate calculations.
• Round all answers to 2 decimal places unless otherwise specified. DO NOT round intermediary
calculations.
• Answer Section A on the MCQ sheet provided; Sections B in a separate answer book, Section C in a
separate answer book and then Section D and Section E in one answer book. You should hand in 3
answer books in total.
• Start section E on a NEW page in your third answer book.
• For all MCQ questions, select the MOST correct answer.
Section A: MCQ [34]
Question 1 (2)
Which of the following is NOT a one-way ANOVA assumption ?
A) Observations are approximately normally distributed.
OB) Each treatment level has the same number of replicates.
C) Observations come from a distribution with equal population variances.
D) Observations are independent of one another.
E) C and D
Question 2 (2)
Which of the following IS a type of experimental design ? ANOVA
A) A completely randomised design RD one way
two ANOVA
B) A blocking ANOVA
C) A two-way design Read wayANOVA
two
D) A and C factorial way
E) A, B and C x
Design with interaction
Question 3 (2)
Factor A and Factor B are said to interact if:
A) Factor A is independent of Factor B.
B) Factor B has a different effect on the response variable depending on the level of Factor A.
C) The level of Factor A changes for different levels of Factor B.
D) Factor A has a different effect on the response variable depending on the level of Factor B.
E) B and D
Page 1
, Stat SStrt t SSresid
Question 4
SStot SStr t t SSblock SSresid
(2)
Adding a blocking variable to a completely randomised design will always have the following effect on the results
of an ANOVA:
O
A) Reduce the residual variation. V ft 9
B) Reduce the F-statistic of the treatment variable.
x
C) Increase the number of experimental units required.
D) Reduce the F-statistic of the blocking variable.
Insite
E) Increase the number of replicates in the experiment.
variable inCR
no
blocking
qÉÉÉ
Question 5
Multiple linear regression analysis is applicable when:
(2)
A) All of the independent variables are continuous.
B) The dependent variable is binary, whilst the independent variables are continuous only.
C) The dependent variable is continuous, and there is only one independent variable.
D) The dependent variable is continuous, and there are many independent variables which are either
continuous or categorical in nature.
E) The dependent variable is continuous, and there are many independent variables which are only
continuous in nature.
Question 6 (2)
A person, who has been vaccinated for malaria, recently visited Nigeria. After reporting this to a doctor at a regular
check-up appointment, the doctor still insisted on performing a malaria rapid diagnostic test. The test result came
out to be positive, even though the person actually does not have malaria. This is an example of:
A) A positive predicted value
B) A false negative
C) A false positive
D) A negative predicted value
E) None of the above
Question 7 (2)
If the coefficient of determination is 0.7510, what is the correlation coefficient value?
A) 75.10%
Tio
B) 56.40%
0C) 86.66%
D) 50.00%
866602
E) There is not enough information to calculate this value. 0
Question 8 (2)
Given the below confusion matrix and assuming disease (coded as 1) is the outcome of interest, compute the
positive predictive value (PPV) and negative predictive value (NPV).
OBSERVED
Disease No disease
ppr s
Disease 107 25
8 89
PREDICTED
a
NPV
No disease
Female 13 89
c d
Page 2
, A) PPV = 89.17% and NPV = 78.07%
B) PPV = 81.06% and NPV = 78.07%
C) PPV = 78.07% and NPV = 89.17%
D) PPV = 87.25% and NPV = 81.06%
E) PPV = 81.06% and NPV = 87.25%
Study the output of an exponential smoothing model below and then answer Questions 9 to 11.
A o 5611 18820 t
1 0.56117 19.568910.4046
19.76
0.3454 21.7005 21,3394 t
1 0.34547 0.4030
0.3885
0.0002 5.4748 t
1 00002 0.9020
0 9020
D 292412 3 0.8007
XO 9882
31.2 699
Question 9 (2)
If you were to apply moving average smoothing with a value of k = 3 to the original time series data, what would
be the first and third smoothed values?
A) 58.42; 76.17
1768 206
11 20
B) 19.47; 20.77 1st 19.47
C) 17.68; 25.38
20.14 22
D)
E)
19.47; 25.39
A; 20.46 3rd 19.31
39 20.77
Page 3
