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STAT 350 Assignment 7 Solutions
(45 points)
22.
(4)
In this problem, we have
507
n
and ˆ
142 / 507
.28008
p
.
For a twosided 99% confidence interval, we
use
*
2.575
z
:
ˆˆ
(1
)
ˆ
*
p
p
n
pz
.28008(1 .28008)
507
.28008
2.575
.28008 2.575(.0199)
(.228, .331)
25.
(a)
(3)
Following the same format used for most confidence intervals, i.e.,
statistic
(critical value) (standard
error),
an interval estimate for
1

2
is:
112 2
12
)
)
()
p
pp
p
z
nn
.
(b)
(4)
The response rate for noincentive sample: p
1
= 75/110 = .6818, while the return rate for the incentive
sample is p
2
= 66/98 = .6735.
Using z = 1.96 (for a confidence level of 95%), a twosided confidence interval
for the true (i.e., population) difference in response rates
1

2
is:
(.6818  .6735)
(1.96)
98
)
6735
.
1
)(
6735
(.
110
)
6818
.
1
(
6818
.
= .0083
.1273 =(.119, .1356).
The fact that this interval contains 0 as a plausible value of
1

2
means that it is plausible that the two proportions are equal.
Therefore, including incentives in the
questionnaires does not appear to have a significant effect on the response rate.
(c)
(4)
Let
i
p
~
denote the sample proportion by adding 1 success and 1 failure to the
i
th
sample.
We calculate
)
2
/(
)
1
(
~
n
x
p
i
, where
x
is the number of successes (or failures, whichever is desired) in the sample.
Then:
67857
.
)
2
110
/(
)
1
75
(
~
1
p
and
.
67
.
)
2
98
/(
)
1
66
(
~
2
p
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 Spring '08
 Staff
 Statistics

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