Concordia University
Department of Economics
ECON 221/4 – Sections AA, B, E
Instructors: M. DaPalma, V. Terekhov, G. Tsoublekas
Winter 2007  ASSIGNMENT 4  Answers
Due at noon on Thursday, April 5, 2007
1.
A cellular phone company advertises that the average age of its customers is fewer than 30.
It is known
that the customer ages follow a normal distribution.
A random sample of 16 of this company’s customers
responded as follows, when asked about their age:
35, 19, 25, 33, 32, 51, 65, 43, 44, 29, 33, 21, 34, 30,
25, 57.
(30 points)
a.
Calculate the sample mean and sample variance.
(5 points)
36
16
576
=
=
=
∑
n
X
X
i
91
.
12
67
.
166
1
16
2500
1
)
(
2
2
=
⇒
=

=


=
∑
s
n
X
X
s
i
b.
Develop an appropriate hypothesis to test the company’s claim at the 5% level of significance. (5 pts)
H
0
:
μ <
30
H
1
:
μ > 30
Reject H
0
if estimated
t > 1.753
859
.
1
2275
.
3
6
4
91
.
12
6
16
91
.
12
30
36
=
=
=

=

=
n
s
X
t
μ
and
1.859 > 1.753
Therefore, we reject
0
H
and we conclude that the average age of the company’s clients is more
than 30.