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1
of
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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.

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- Fall '10
- A.Stawinoga
- Standard Deviation, Variance, Type I and type II errors, tail test
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