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Solutions to Homework 9
Problem 8.29
a. We can compute
n
:
n
=
z
2
α/
2
σ
2
E
2
=
1
.
96
2
6
.
25
2
2
2
= 37
.
5
.
So we should sample at least 38.
b. We can compute
n
:
n
=
z
2
α/
2
σ
2
E
2
=
1
.
96
2
6
.
25
2
1
2
= 150
.
06
.
So we should sample at least 151.
Problem 8.35
a. The point estimate of the proportion of oﬃce workers who are able to take every
telephone call is
281
611
= 0
.
46
.
b. The margin of error for a 90% conﬁdence interval is
z
α/
2
s
¯
p
(1

¯
p
)
n
= 1
.
645
s
0
.
46(1

0
.
46)
611
= 0
.
033
.
c. The 90% conﬁdence interval is
¯
p
±
z
α/
2
s
¯
p
(1

¯
p
)
n
= 0
.
46
±
0
.
033 = (0
.
427
,
0
.
493)
.
Problem 8.39
a. Here we will use
p
*
= 0
.
156,
E
= 0
.
03 and
z
α/
2
= 1
.
96. The required sample size is
n
=
(
z
α/
2
)
2
p
*
(1

p
*
)
E
2
=
(1
.
96)
2
(0
.
156)(1

0
.
156)
0
.
03
2
= 562
.
0
.
We would sample at least 562 individuals.
b. The only diﬀerence from part a is that
z
α/
2
= 2
.
575. The required sample size is
n
=
(
z
α/
2
)
2
p
*
(1

p
*
)
E
2
=
(2
.
575)
2
(0
.
156)(1

0
.
156)
0
.
03
2
= 970
.
01
.
We would sample at least 971 individuals.
1
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View Full DocumentProblem 8.43(b,c)
b. We have ¯
p
= 0
.
31 and
n
= 1500. The margin of error for a 95% conﬁdence interval is
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 Spring '10
 Jager,AbigailL

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