MSIN2003: Business Analytics
FINAL EXAMINATION PAPER
10 December 2014
The final examination will last two (2) hours.
There are two (2) parts to the examination paper.
Answer ALL questions in Part A and Part B.
The total value of the questions from Part A count for 20 (TWENTY) marks, and Part B for
80 (EIGHTY) marks.
The value of each question is provided in square brackets.
Please do read the instruction for each part carefully.
IMPORTANT NOTES:
This is a closed-book, closed-notes exam.
Laptops, mobile devices, and any electronic communications devices are NOT permitted.
However, you are allowed to take one-page two-sided A4 paper with anything you would
like to write.
Calculators are permitted.
Z- and t-distribution tables are provided on pages 12 and 13 of the exam.
Please write your answer to each question in the exam paper, below the question.
If you need more space, you may use the last four pages of the exam. In this case, indicate
clearly in the designated space under each section where you continued your solution.
You are NOT allowed to take away the exam paper from the exam room.
It is suggested that you split your time between the sections as follows:
Part A: 20 minutes
Part B:
Question 1: 35 minutes
Question 2: 35 minutes
Question 3: 30 minutes
Part A - Answer all questions by indicating whether the statements are
TRUE or FALSE (T/F).
The value of each questions is 2 marks. You may do calculations in the space provided if
necessary. However, marks will be awarded only for the right answer, true or false.
1. (T/F) If P(B)≠0 then P(Bc|B)=0.5.
2. (T/F) Let A and B be two companies. Assume that the expected return of
company A is equal to the expected return of company B, and that the variance of
the returns of A is four times larger than the variance of the returns of company B.
Then the return-to-risk ratio of company A is four times smaller than the return-
to-risk ratio of company B.
3. (T/F). Let X be a discrete random variable, and let Y=3X+15. Then
E[Y]=3E[X]+15.
4. (T/F) If X~U(50,120) then P(25≤X≤60)=0.35.
5. (T/F) If Z~N(0,12) then P(Z<0.44)=0.67.
6. (T/F) Assume that the mean of a certain property of a population is μ, and that its
standard deviation is ϭ. If the sample size, n, is larger than 30, then the sample
mean’s distribution tends to a normal distribution with mean μ and standard
deviation 𝝈√𝒏..
7. (T/F) A (1-α)∙100% confidence interval for μ when ϭ of the population is known
is: [𝐗̅−𝐭𝛂/𝟐 𝐒√𝐧,𝐗̅+𝐭𝛂/𝟐 𝐒√𝐧].
8. (T/F) In a one left-tailed test, the hypotheses are:
H0: μ≥M,
H1: μ
9. (T/F) Let X1 and X2 be prices of two competing products. 50 prices of each of the
products were sampled on 50 different days. You would like to test the
hypotheses:
H0: 𝛍𝐗𝟏 = 𝛍𝐗𝟐,
H1: 𝛍𝐗𝟏 ≠ 𝛍𝐗𝟐.
You ran a two-sample t-test assuming unequal variances in Excel. The following
results were obtained:
If α=0.05, then H0 should be accepted and H1 rejected.
10. (T/F) Let X, Y, and Z be random variables. If the correlation between X and Z is
-0.7, and the correlation between Y and Z is 0.5, then the percentage of the
variance in Z which is explained by Y is larger than the percentage of the variance
in Z which is explained by X.
Part B - Answer all questions.
YOU MUST SHOW ALL YOUR WORK.
CLEARLY INDICATE YOUR FINAL ANSWER AND CONCLUSION.
The value of each question is provided in square brackets.
1. [30 marks] Imagine that you are a restaurant manager.
a. Each day, 15 people come to your restaurant for lunch. The probability that
each diner orders pizza as a main course is 0.6. Assume that the customers’
orders are independent, and that each customer orders only one main course.
What is the probability that the number of pizzas ordered during a single lunch
is 12? Explain the notation you use and show all your work.
b. The main ingredients of a basic (Margherita) pizza are flour, cheese, and
tomato sauce. Assume that each pizza contains 250 gr flour and 150 gr cheese.
The price of a pack of 500gr of flour has mean £0.5 and variance £0.1. The
price of a pack of 150gr cheese has mean £1 and variance £0.24. Assume that
the price of tomato sauce is £0.5 and that all prices are normally distributed
and independent.
i. Find the distribution of the total price of the main ingredients of a basic
pizza. Report the distribution’s mean and standard deviation.
ii. What is the probability that the total price of the main ingredients of a
basic pizza is higher than £2.8?
CANDIDATE NUMBER: _______________________
iii. Consider the price of pizza toppings ordered by diners. The mean price
of the toppings, obtained by sampling it in 30 randomly chosen days,
was £2. The standard deviation obtained in the sample was £0.4.
Assume that toppings’ price follows a normal distribution. Find a 95%
confidence interval for the mean price of pizza toppings ordered by
diners.
Explain each stage in your solution. If you use variables, explain their
meaning.
2. [30 marks] A manager in a high-tech company wants to assess the effect of the
amount of money invested in Research and Development (R&D) on sales volume.
To do so, he collects information about four different products. The amount of
money invested in R&D for each product and the number of sold units of each
product are presented in the following table.
Product number X- The amount of money
invested in R&D (in
thousands of pounds)
Y- The number of sold
units (in thousands)
1 10 20
2 18 32
3 36 85
4 40 75
a. Calculate a linear regression model for the number of sold units (in thousands),
using the amount of money invested in R&D as the predictor. You can use the
information that
SSxy = ∑(xi −X̅)(yi −Y̅)
n
i=1
= 1324.
b. The company invested £20,000 in the R&D of a new product. What is the number
of units of the new product which will be sold, according to the model you found
for Section a?
c. It was found that for the given data, ∑ yi24i=1 − 14(∑ yi4i=1 )2 = 3038. Is the slope
you obtained for the model in Section a significantly different from 0?
Write the corresponding hypotheses, calculate the relevant statistic and test value,
and draw a conclusion. Use significance level α=0.01.
3. [20 marks] A financial forecasting firm develops a model to predict whether the
Dow Jones Industrial Average (DJI) would increase or decrease.
a. The model predicts that DJI increases with probability 0.70 when it increases. It
predicts that DJI increases with probability 0.20 when it does not increase
(decreases or remains the same). Assume that the probability that the DJI
increases is 0.6. If the model predicts that the DJI increases, what is the
probability that it would indeed increase?
b. A financial analyst working at this company suggests to examine the
efficiency of the model:
𝑌 = β0eβ1X1eβ2X2ε,
where X1 represents time, X2 represents the inflation rate and Y represents the
DJI values.
How can you transform. this model to a linear model? What would be the
variables of the linear model? Submit each stage of the development of the new
model and the variables.
c. A different analyst is interested in the correlation between the DJI and
S&P500 indices. Data about these two indices was collected. Denote by X the
DJI prices and by Y the S&P500 prices. It was found that
SSX,Y=49,578,937.44, SSX=405,718,764, SSY=6,144,891. Calculate the
correlation between the DJI and the S&P500.