WU Data Science and Analytics Questions – Description
Problem 1 [18 Marks]
Date on the tab “Problem_1_Data” contains fic��ous data on over 2000 customers of Hutchison 3G
UK Ltd, a Bri�sh telecommunica�ons and internet service provider. Each row contains the ac�vity of a
specific customer for a given �me period, and the last column indicates whether the customer
‘churned’ during this �me period. Churning occurs when a customer stop using one company’s service
and switches to another company’s service. Answer the following ques�ons:
a. How are the variables distributed? [3]
b. How are the variables in columns B-R related to each other? [4]
c. How are the variables in columns B-R related to the Churn variable in column S? [6]
d. Write a report of your findings, including any recommenda�ons you would make to the
company to reduce churn. [5]
Problem 2 [14 Marks]
Asma Ali is the owner of a small electronica company. In six months, her company is scheduled to put
in a proposal to upgrade the electronic informa�on systems across all TFL sta�ons in Southeast
London. Ali’s company has been developing a new microprocessor which is a cri�cal component of the
new electronic informa�on system that would be superior to any product currently on the market and
could lead to future contracts covering the rest of London. However, progress in research and
development has been slow, and Ali is unsure whether her staff can produce the microprocessor in
�me. If her company succeeds in developing the microprocessor (p1), there is an excellent change
(probability p2) that Ali’s company will win the £1 million TFL contract. If not, there is a small chance
(probability p3) that she will s�ll be able to win the same contract with an alterna�ve but inferior
informa�on system that has already been developed.
If Ali con�nues the project, she must invest £200,000 in R&D. In addi�on, preparing a proposal (which
she will decide whether to do a�er seeing if the R&D is successful) requires developing a prototype
informa�on system at an addi�onal cost. This addi�onal cost is £50,000 if R&D is successful (so she
can develop the new system) and it is £40,000 if R&D is unsuccessful (she will need to go with the older
system). Finally, if Ali wins the contract, the finished product will cost an addi�onal £150,000 to
produce.
a. Develop a decision tree that can be used to solve Ali’s problem. You can assume in this part of
the problem that she is using EMV (of net profit) as a decision criterion. Build the tree so that
she can enter any values for p1, p2, and p3 (in input cells) and automa�cally see her op�mal
EMV and op�mal strategy from the tree. [5]
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b. If p2 = 0.8 and p3 = 0.1, what values of p1 makes Ali indifferent between abandoning the project
and going ahead with it? [2]
c. How much would Ali benefit if she knew for certain that TFL would guarantee her the contract?
(This guarantee would be in force only if she were successful in developing the product.)
Assume p1 = 0.4, p2 = 0.8, p3 = 0.1. [2]
d. Write a report of your findings, including any recommenda�ons you would make to the
company to Asma. [6]
Problem 3 [21 Marks]
The Greenwich branch of Tesco, a groceries and general merchandise retailer, are examining their
delivery data. Most of their deliveries are within a 10-mile radius, but they occasionally deliver to
customers more than 10 miles away. Tesco employs a number of delivery people, four of whom are
rela�vely new hires. The grocery chain has recently been receiving customer complaints about
excessively long delivery �mes. Therefore, Tesco Greenwich has collected data on a random sample by
its four new delivery people during peak delivery �mes. The data are in the tab �tled
“Problem_3_Data”. The variables are: Deliverer: which person made the delivery; Prep Time: �me
from when order was places un�l delivery person started driving it to customer; Travel Time: �me to
drive from Tesco to customer; Distance: distance (miles) from Tesco to customer. Greenwich Tesco is
concerned that one or more of the new delivery people might be slower than others.
a. Let Di and Ti be the mean delivery �me and mean total �me for delivery person i,
where the total �me is the sum of the delivery and perp �mes. Calculate 95%
confidence intervals for each of these means for each delivery person. Although these
might be interes�ng, give two reasons why they are not really fair measures for
comparing the efficiency of the delivery people. [7]
b. Responding to cri�cism in part a, calculate a 95% confidence interval for the mean
speed of delivery for each delivery person, where speed is measured as miles per hour
during the trip from Tesco to the customer. Then calculate 95% confidence intervals
for the mean difference in speed between each pair of delivery people. [7]
c. Write a report of your findings, including any recommenda�ons you would make to
Tesco. [7]
Problem 4 [24 Marks]
Pfizer has developed a new drug called Pampa, an an�-inflammatory said to alleviate pain from
arthri�s and other painful afflic�ons. This drug is currently being marketed heavily as a new
blockbuster and is being prescribed widely. However, not too long ago, a large study uncovered some
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worrying risk factors. This study had 1287 pa�ents use Pampa for an 18-month period, and it had
another 1299 pa�ents use placebo over the same period. A�er 18 months, 45 of the Pampa pa�ents
had developed serious heart problems, whereas only 25 pa�ents on the placebo developed such
problems. Data is provided in the datafile under tab “Problem_4_Data”.
a. Given these results, would you agree with the conclusion that Pampa caused significant
increase in the risk of developing serious heart problems? First, answer this from a purely
sta�s�cal point of view, where significant means sta�s�cally significant. What hypothesis
should you test, and how should you run the test? When you run the test, what is the
corresponding p-value? [7]
b. Next, look at it from the point of view of pa�ents. If you were a Pampa user, would these
results cause you significant worry? A�er all, some of the subjects who took placebos also
developed heart problems, and 45 might not be considered that much larger than 25. [7]
c. Finally look at it from Pfizer’s point of view. Are the results prac�cally significant to the
company? What does it stand to lose? [5]
d. Write a report of your findings and interpret the results based on the discussion points from
ques�ons a, b & c. [5]
Problem 5 [22 Marks]
The Charring Cross branch of NatWest is having trouble ge�ng the correct staffing levels to match
customer arrival paterns. On some days, the number of tellers was too high rela�ve to customer
traffic, so that tellers were o�en idle. On other days, the opposite occurred. Long customer wai�ng
lines formed because the rela�vely fewer tellers could not keep up with the number of customers. The
manager, Michael Kaluuya, knew that there was a problem, but he had litle of the quan�ta�ve training
he believed would be necessary to find a beter staffing solu�on. Michael figured that first, he needed
a reliable forecast of each day’s number of customer arrivals. Data for this problem is in the dataset
file under the tab “Problem_5_Data”. The data lists the number of customers entering this bank each
day of the past year. It also lists other informa�on: the day of the week, whether the day was a staff or
faculty holiday.
a. Use this data set to develop a forecas�ng models that Michael could use to help solve this
problem. [Hint] You will need to create Dummy Variables [8]
b. Develop an improved model using only significant variables. Comment on your results and
poten�al issues. [7]
c. Based on your model(s), write a report and make any recommenda�ons about staffing that
appear reasonable.
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