Mid-Term_-_Solutions - UNIVERSITY OF TORONTO QUANTITATIVE...

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U
NIVERSITY OF
T
ORONTO
Q
UANTITATIVE
M
ETHODS IN
E
CONOMICS
II
ECMB12H3F (LEC02)
M
ID
-
TERM
T
EST
– S
OLUTIONS
D
URATION
: 90
MINUTES
O
CTOBER
20, 2010
I
MPORTANT
:
(i) This test should be answered in BALLPOINT PEN and students who attempt the test in
pencil would surrender their rights to request for re-assessment.
(ii) Ensure HANDWRITING is LEGIBLE and show STEP-BY-STEP CALCULATIONS .
Answer all questions only in the DESIGNATED PAGES . ROUGH WORK should be
done in the LAST TWO PAGES and contents in those pages will not be graded.
(iii) AIDS ALLOWED – a HAND-WRITTEN SINGLE-SIDED LETTER SIZE CRIB
SHEET (photocopies or printed copies not allowed) and a NON-PROGRAMMABLE
CALCULATOR (other electronic devices with calculator functions not allowed).
(iv) DO NOT SEPARATE any page from this test.
Student Name
Student ID#
Question 1 2 3 4 5 Total
Marks 17 31 20 12 20 100
Score

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1. As the vice president in operations of a major fast food chain, the current average time to
serve a customer using the drive-thru service is 3 minutes and you are interested in cutting
down the average time by installing a new automated self-serve system, which costs
millions of dollars. The new system has been tested in a particular location where it served
a sample of 64 customers and the average time is 2.75 minutes with a standard deviation of
1 minute. (i) Follow the six-step critical value approach to hypothesis testing at 5% level
of significance with the sample data to determine whether to invest in this new automated
self-serve system or not. (ii) Can you determine the range of the -value of the test
statistic?
(i) 12 marks and (ii) 5 marks
(i) Step 1 – the company will only invest in the new automated self-serve system if it can
significantly reduce the average time to serve customers using the drive-thru service, which
implies a one tail test.
and
Step 2 – the level of significance is 5% and the sample size .
Step 3 – only the -test is appropriate where there is no information about the population
variance.
Step 4 – for and with degrees of freedom , the critical value
for the one tail test is .
Step 5 – with sample statistics , , and . The test statistic
Step 6 – since and it is less than the critical value of , the test statistic
falls in the rejection region and hence the null hypothesis is rejected. There is enough
evidence to conclude that the average time to serve a drive-thru customer is significantly
less than 3 minutes and hence it is worthwhile to invest in the new automated self-serve
system.