# Statistics Exam Paper

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08 ETHE AUSTRALIAN NATIONAL UNIVERSITY
SCHOOL OF FINANCE AND APPLIED STATISTICS
First Semester Examination 2010

QUANTITATIVE RESEARCH METHODS
(STAT1008)
Writing Period: 3 hours duration
Study Period: 15 minutes duration
Permitted Material: Non-programmable calculator, dictionary and 1 A4 page with notes on both sides

Instructions to Candidates:
• Attempt ALL questions.
• Each question is of equal mark value.
• Start your solution to each question on a new page.
• To ensure full marks show all the steps in working out your solution. Marks may be deducted for failure to show appropriate calculations or formulae.
• Unless otherwise stated, use a significance level of 5%. • Selected statistical tables are attached to the back of the examination paper.

Page 1 of 9

Question 1 (25 marks)
Many companies have invested in automated customer-service systems for phone calls, primarily because the cost of a phone call passed on to a live operator is approximately ten times that of a call answered by an automated system. However, many customers dislike automated systems, and will choose the first offered option to speak with a live person, for example, pressing “0” at the “Press 0 to speak with a customer service representative”. Research shows that approximately 40% of callers to automated systems will automatically opt to speak to a live operator when given the chance.

Imagine that 10 independent callers contact an automated customer service system. (a) (3 marks) What type of random variable is the number of callers who automatically opt to talk to a live operator? Give the appropriate parameters of the random variable.

(b) (1 mark) What is the probability that none of them automatically opts to talk to a live operator?
(c) (1 mark) What is the chance that 3 or fewer will automatically opt to talk to a live operator?
(d) (2 marks) What is the chance that exactly 3 will automatically opt to talk to a live operator?
(e) (4 marks) What is the expected number who will automatically opt to talk to a live operator? What is the standard deviation of the number who will automatically opt to talk to a live operator?

(f) (4 marks) In a different study, 90 random callers were tracked, and it was found that 45 automatically opted to speak with a live operator. Using a confidence interval, determine if the claim of 40% above is supported by this data, with a 5% significance.

Another variable of interest is the length of time people wait on hold before speaking with an operator. For one particular call centre, it is known that the length of time on hold is a uniformly distributed variable with minimum 85 seconds, and expected value of 120 seconds.

(g) (3 marks) Write an equation and draw a graph representing the distribution of the length of time on hold.
(h) (3 marks) What is the standard deviation of the length of time on hold? (i) (4 marks) The length of time on hold is recorded for 80 separate callers to the call centre, and the average calculated. Find the probability that the average length of call is longer than 130 seconds.

STAT1008 Quantitative Research Methods Final Examination Semester 1, 2010 Page 2 of 9

Question 2 (25 marks)
A busy Sydney car yard has records of selling performance of salespeople employed in the yard. After a particularly difficult selling month, the manager wishes to analyse staff performance to determine which features, if any, could be used to predict the number of sales made in the previous month. The predictor variables to be used are the years of experience selling cars of the salesperson, and the number of different types of products the salesperson has sold in the past.

Scatterplots are shown below of the response variable (number of sales made last month) against each of the predictors, for the 47 salespeople in the yard. Scatterplot of Number of Sales last month vs Years of experience

Number of Sales last month

60

50

40

30

20

10

0
0

5

10...