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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 reassessment.
(ii)
Ensure
HANDWRITING
is
LEGIBLE
and show
STEPBYSTEP 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
HANDWRITTEN SINGLESIDED LETTER SIZE CRIB
SHEET
(photocopies or printed copies not allowed) and a
NONPROGRAMMABLE
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 drivethru service is 3 minutes and you are interested in cutting
down the average time by installing a new automated selfserve 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 sixstep critical value approach to hypothesis testing at 5% level
of significance with the sample data to determine whether to invest in this new automated
selfserve 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 selfserve system if it can
significantly reduce the average time to serve customers using the drivethru 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 drivethru customer is significantly
less than 3 minutes and hence it is worthwhile to invest in the new automated selfserve
system.
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 Fall '10
 A.Stawinoga
 Standard Deviation, Variance, Type I and type II errors, tail test

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