Jun 06, 2017

Use a simple example to demonstrate the meaning of spurious correlation.

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QUANTITATIVE METHODS FOR MANAGERS

Instructions to candidates:

a) Time allowed: Three hours (plus an extra ten minutes’ reading time at the start – do not write anything during this time)

c) All questions carry equal marks. Marks for each question are shown in [ ]

d) Non-programmable calculators are permitted in this examination

1. a) Use a simple example to demonstrate the meaning of spurious correlation. [5]

b) The personnel department of a large marketing organisation holds regular interview days where potential candidates are required to undergo an interview and a numeracy test. The results for one particular session are shown in the following table:

 Candidate A B C D E F G H Interview rank 5 1 3 2 6 8 7 4 Numeracy test score 70 85 80 75 60 60 58 83 Calculate the Rank Correlation Coefficient, and use this to comment on the level of agreement between the interview and testing process .

2. A large builders’ merchant has estimated that the number of days between sending out a monthly invoice and receiving the payment from its customers is normally distributed with a mean of 16 days and a standard deviation of 4 days.

a) Find the probability that an invoice will not be paid until after 18 days. [5]

b) From 200 invoices, how many would be expected to be paid between 12 days and 22 days? [8]

c) As an incentive to pay early, the company offers to reward the quickest 10% of customers with a

5% discount on their bills. On what day should the incentive be set? [7]

3. The customer helpline of an insurance company operates from Monday to Friday. As part of a quality assurance exercise, the company monitors the calls to the helpline over a period of three weeks, and the following table shows the results of this exercise:

 Week 1 2 3 Day M Tu W Th F M Tu W Th F M Tu W Th F No. of enquiries 33 41 77 81 99 39 49 84 90 107 47 55 91 102 113 a) Plot a graph of the above time series, and comment on any movements that are present. [4]

b) Using the above graph, decide what will be the most appropriate moving average, and use this to superimpose the trend line on your graph. [8]

c) Calculate the seasonal component for Monday. [5]

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