UNIVERSITY OF MAURITIUS
FACULTY OF LAW AND MANAGEMENT
FIRST SEMESTER EXAMINATIONS
FEBRUARY 2021
BSc (Hons) Accounting (Minor: Finance) – Level II,
III (Part-Time)
PROGRAMME
BSc (Hons) Finance – Level I
BSc (Hons) Finance (Minor: Law) – Level I
MODULE NAME
STATISTICS FOR FINANCE
DATE
Wednesday
24 February 2021
MODULE CODE
STAT1004 (1)
TIME
13:30 – 15:30 Hours
DURATION
2 Hours
4
NO. OF QUESTIONS
TO BE ATTEMPTED
3
NO. OF
QUESTIONS SET
INSTRUCTIONS TO CANDIDATES
This paper consists of 25 MCQs, 4 questions and 2 Sections (Sections A
and B).
Section A is Compulsory and consists of 25 MCQs. Students are requested
to answer MCQs on the Answer Sheet provided.
Answer ANY TWO (2) questions from Section B. Each question carries 35
marks.
Silent non programmable calculators are allowed.
List of statistical formulae and statistical table are provided.
5 marks will be allocated for the proper presentation of your work.
Statistics for Finance – STAT1004 (1)
SECTION A (COMPULSORY)
This section consists of 25 MCQs. Students are requested to answer MCQs on the
Answer Sheet provided.
Question 1
1.01
Random sampling implies that individuals in a sample are chosen haphazardly to
avoid bias? True or False?
A. True
B. False
1.02 The rate of change in the S&P 500 index on 01 October 2014 was -0.28%. The rate of
change in S&P 500 index is classified as what type of data?
A.
B.
C.
D.
1.03
Nominal
Ordinal
Continuous.
Discrete
The histogram below shows the class test scores of a group of 90 students of the
module STAT 7010.
Which of the following statements is correct?
A. The distribution is skewed to the right
B. The distribution is skewed to the left
C. The distribution appears to be symmetrical
D. None of the above
Page 1 of 8
Statistics for Finance – STAT1004 (1)
Questions 1.04 and 1.05 refer to the following situation. The average monthly salary of 70
employees in an organisation is Rs 30500 and the median salary of the employees is
Rs 28000.
1.04
What is the total monthly salary paid to the employees?
A.
B.
C.
D.
1.05
Which of the following statement is true?
A.
B.
C.
D.
1.06
Rs 2135000
Rs 435.71
Rs 2530460
None of the above
The distribution of salary is positively skewed.
The distribution of salary is negatively skewed.
50% of employees obtain a salary of Rs 28000
None of the above
IQ scores from an IQ test follow a normal distribution with mean 100 and variance
15.
What is the probability that a random selection of 50 individuals will have mean IQ
scores above 101?
A. 0.0340
B. 0.0983
C. 0.2462
D. None of the above
1.07
Correlation implies causality. True or False.
A. True
B. False
1.08
Consider the following information which relates to the monthly salary of workers
for two companies.
Mean
Standard Deviation
Company A
Rs 23,000
Rs 10,000
Company B
Rs 25,000
Rs 10,500
Which of the following statements is correct?
A. The average salary of company A is higher than company B
B. The salary of employees for Company B shows higher variation compared to
company A
C. The salary structure of company B is more negatively skewed than that of
company A
D. None of the above.
Page 2 of 8
Statistics for Finance – STAT1004 (1)
1.09
Which of the following distributions is appropriate to model the number of patients
admitted to a regional hospital each day with a particular rare disease?
A. Poisson
B. Binomial
C. Normal
D. None of the above
1.10
The expected value of a discrete random variable
A. is the outcome that is most likely to occur.
B. can be found by determining the 50% value in the cumulative distribution
function.
C. equals the population median.
D. is computed as a weighted average of the possible outcome of that random
variable, where the weights are the probabilities of that outcome.
1.11
Three confidence intervals for the mean shear strength (in ksi) of anchor bolts of a
certain type are computed, all from the same sample. The intervals are (4.01, 6.02),
(4.20, 5.83), and (3.57, 6.46). The levels of the intervals are 90%, 95% and 99%. Which
interval has which level?
A.
B.
C.
D.
1.12
(4.01, 6.02) – 90%, (4.20, 5.83) – 95%, and (3.57, 6.46) – 99%
(4.01, 6.02) – 95%, (4.20, 5.83) – 90%, and (3.57, 6.46) – 99%
(4.01, 6.02) – 99%, (4.20, 5.83) – 95%, and (3.57, 6.46) – 90%
None of the above
A correlation coefficient of
is correct?
= −0.5 is computed. Which of the following statements
A. The independent variable explains 25% of variation in the dependent variable
B. The independent variable explains - 25% of variation in the dependent variable
C. The independent variable explains 50% of variation in the dependent variable
D. None of the above.
1.13
An economic advisor studies the effect of a policy decision on workers of the
manufacturing industry. He is essentially concerned with those who have been laid
off from their work. He takes a random sample of the number of workers laid off
from each of 144 factories. The corresponding sample mean number of workers laid
off is 55.2 and the sample standard deviation is 5.87.
Estimate the true mean number of workers laid off.
A. 5.87
B. 34.5
C. 50
D. 55.2
Page 3 of 8
Statistics for Finance – STAT1004 (1)
1.14
Products produced by a machine have a 1% defective rate. What is the probability
that the first defective occurs on the fourth item inspected?
A.
B.
C.
D.
1.15
0.0097
0.0388
0.0029
None of the above
The function ( ) = 0.5 for 2 <
< 4 is a valid pdf. True or False?
A. True
B. False
1.16
Reliability is a desirable property of a point estimator. True or False?
A. True
B. False
1.17
P(A ∩ B ) =? ? ?
A. P(B)
B. P(A|B′)- P(A′|B′)
C. P(A) − P(A ∩ )
D. None of the above
1.18
A representative from the Premier League's Marketing Division randomly selects
people on a random street in Liverpool City, England until he finds a person who
attended the last home football game. The probability that he succeeds in finding
such a person is 0.20. What is the probability that the marketing representative must
select 5 people before he finds one who attended the last home football game?
A.
B.
C.
D.
1.19
0.1024
0.0655
0.0819
None of the above
Events A and B are such that
( )=
1
1
, ( )=
2
3
( ∪ )=
3
4
A. Both A and B are mutually exclusive
B. Both A and B are independent.
C. They are both mutually exclusive and independent.
D. None of the above.
1.20
When the occurrence of an event B has no effect on the probability of occurrence or
non-occurrence of A (or, vice versa), then A and B are said to be ………….. events.
A. mutually exclusive
B. independent
C. complementary
D. None of the above
Page 4 of 8
Statistics for Finance – STAT1004 (1)
1.21
In a certain country, the weather on any day is dry with probability 1/3 and wet with
probability 2/3, the weather on different days being independent. What is the
probability that the next three days are dry?
A.
B.
C.
D.
1.22
1/27
26/27
1/3
None of the above
A candle manufacturer wants to state an average burning time on the packaging of
his perfumed candles. He records the burning times for a random sample of 15
candles and enters the data into a computer package, which tells him that a 90%
confidence interval for the mean burning time is from 48.388 hours to 56.012 hours.
What is the standard error of the mean burning time for the sample of 15 candles?
A. 52.20
B. 8.382
C. 2.164
D. None of the above
1.23
A 10-question multiple choice class test is given, and each question has four possible
answers where only one answer is correct per question. Julie takes this exam and
guesses at every question. To pass the class test, she has to score at least four correct
answers. What is the probability that she fails the class test?
A. 0.224
B. 0.25
C. 0.776
D. None of the above
1.24
A washing machine in a Laundromat breaks down an average of three times per
month. Using the Poisson probability distribution, find the probability that during
the next month this machine will have at most one breakdown.
A.
B.
C.
D.
1.25
0.1991
0.8001
0.1494
None of the above
From past experience it is known that 3% of accounts in a large accounting
population are in error. What is the probability that 5 accounts are audited before an
account in error is found?
A. 0.859
B. 0.885
C. 0.027
D. None of the above
[TOTAL: 25 marks]
Page 5 of 8
Statistics for Finance – STAT1004 (1)
SECTION B
Answer ANY TWO (2) questions.
Question 2
(a)
The yearly average yield (%) on Real Estate Investment Trust (REIT) and Bonds for
twenty years have been arranged in the following frequency table.
Yield (%)
-40 but under -25
-25 but under -10
-10 but under 5
5 but under 20
20 but under 35
35 but under 50
Frequency (REIT)
1
2
3
7
5
2
Frequency (Bonds)
1
1
7
8
2
1
(i)
Without performing any calculations, what can you say about the
distributions of yield for REIT and Bonds?
[2 marks]
(ii)
The mean and the variance for the yearly average yield (%) for Bonds are 6.5
and 256.5 respectively.
Compute the mean, median and standard deviation of REIT only. [11 marks]
(iii)
Compute the Pearson’s coefficient of skewness of the distribution on yield for
REIT only?
[3 marks]
(iv)
Compare the variation in the yield on REIT and Bonds.
[3 marks]
(b)
In a company, parts are produced by two production lines. Line 1 produces
1,000 parts per week of which 100 are defective. Line 2 produces 2,000 parts
per week of which 150 are defective.
If a part is randomly selected from the stock, find the probability that it is
defective.
If the part is defective what is the probability it was produced by line 1?
[6 marks]
(c)
The amount of time (in minutes) a bank clerk spends with a client is known to
follow an exponential distribution with an average of 4 minutes.
(i)
A client is selected at random. Find the probability that the clerk spends four
to five minutes with the client.
[4 marks]
(ii)
Half of the clients are finished within how long?
(iii)
Suppose a client has spent four minutes with the bank clerk. What is the
probability that he or she will spend at least an additional three minutes with
the clerk? Specify the property being used.
[3 marks]
[TOTAL: 35 marks]
Page 6 of 8
[3 marks]
Statistics for Finance – STAT1004 (1)
Question 3
(a)
Describe the following:
(i)
(ii)
(iii)
(iv)
Type I error,
Type II error,
Power of a test,
Significance level.
[8 marks]
(b)
An investor wishes to analyse the overall returns for a stock index that comprises of
1000 equities. It is known that the average and standard deviation of returns for these
1000 equities are 0.1 and 0.02 respectively. What is the probability that a randomly
selected sample of 50 equities across various sectors from the 1000 equities will have
an average return less than 0.095?
[5 marks]
(c)
There are two major competitors in the banking sector for a certain country. An
investor believes that the growth rate per week in the share price for the two banks
are the same. The changes (Rs) in share prices for these two banks over seven weeks
are recorded as follows:
Bank A: 4, 3, 2, 3, 1, 7, 2
Bank B: 3, 1, 4, 3, 2, 6, 4
(d)
(i)
Construct a 95% confidence interval for the difference in the changes in share
prices for the two banks.
[11 marks]
(ii)
Interpret the confidence interval obtained in part (i) and state whether the
belief of the investor is reasonable.
[2 marks]
The average earnings per share for 15 randomly selected stocks of different sectors
from those listed on the Stock Exchange of Mauritius is 1.85 with a standard
deviation of 0.401. An investor claims that the true average earnings per share is 1.90
for all stocks in the market. Is there sufficient evidence to support the claim of the
investor? Test at the 5% level of significance.
[9 marks]
[TOTAL: 35 marks]
Page 7 of 8
Statistics for Finance – STAT1004 (1)
Question 4
The following table gives the advertising expenditure and sales volume for ten consecutive
months.
Month
Advertising Expenditure (Rs 10,000) -X
Sales Volume (Rs 10,000) - Y
1
12.5
115
2
7.5
98
3
10.5
120
4
13
115
5
7.5
95
6
9.7
80
7
8.5
100
8
8
82
9
11
100
10
9.9
105
! "# = $%%&$. ' ; ! ") = **+. ,';
! #) = $%,&)[3 marks]
(a)
State the assumptions of the simple linear regression model.
(b)
Compute the Pearson’s product moment correlation coefficient for the above data
and interpret it.
[6 marks]
(c)
What are the limitations of the Pearson’s product moment correlation coefficient?
[2 marks]
(d)
State a point of caution while interpreting the correlation. Provide two examples to
illustrate the point.
[3 marks]
(e)
Compute the coefficient of determination and interpret your result.
[4 marks]
(f)
Find the least squares regression equation for the above data.
[7 marks]
(g)
Interpret the regression equation obtained in part (f).
[3 marks]
(h)
Provide a justification to support fitting a regression model of the form ./ = + 1 to
these data.
[2 marks]
(i)
Using your answer to part (f), estimate the sales volume in a given month if the
advertising expenditure are
-
Rs 10,000
Rs 5,000
Comment on the reliability of your estimates.
[5 marks]
[TOTAL: 35 marks]
END OF QUESTION PAPER
Page 8 of 8