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

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

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)

b) Answer any FIVE questions

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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