QAS129:001
Instructor: Dr. Yudan Zheng
1.
A real estate company is interested in testing whether, on average, families in Gotham have
been living in their current homes for less time than families in Metropolis have. Assume
that the two population variances are equal.
A random sample of 100 families from Gotham
and a random sample of 150 families in Metropolis yield the following data on length of
residence in current homes.
Gotham:
X
G
= 35 months,
s
G
2
= 900
Metropolis:
X
M
= 50 months,
s
M
2
= 1050
(1)
What are the hypotheses tested by the real estate company?
ANSWER:
H0: ug – um >= 0
H1: ugum < 0
(2)
Which test would likely be most appropriate to employ?
a.
Paired
t
test
b.
Pooledvariance
t
test for the difference between two means
c.
Independent samples
Z
test for the difference between two means
d.
Related samples
Z
test for the mean difference
ANSWER: b
(3)
What is the estimated standard error of the difference between the 2 sample means?
ANSWER:
06
.
4
150
1
100
1
12
.
990
)
1
1
(
12
.
990
)
1
150
(
)
1
100
(
1050
)
1
150
(
900
)
1
100
(
)
1
(
)
1
(
)
1
(
)
1
(
2
1
2
2
1
2
2
2
2
1
1
2
=
+
×
=
+
=

+

×

+
×

=

+


+

=
n
n
S
n
n
S
n
S
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 Fall '10
 Zheng
 Statistics, Null hypothesis, Statistical hypothesis testing, Gotham, real estate company

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