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STAT 100B HWI Solution
Problem 1:
Suppose in a population of voters, the proportion of those who support a candidate is
p
. Suppose we get a random sample of 1000 people, and within this sample, the number of people
who support this candidate is 530.
(1) Calculate the 95% conﬁdence interval for
p
. Calculate the margin of error.
A: ˆ
p
= 530
/
1000 =
.
53. The standard error of ˆ
p
is
p
ˆ
p
(1

ˆ
p
)
/n
=
p
.
53
×
(1

.
53)
/
1000 =
.
0158. The 95% conﬁdence interval is [
.
53

2
×
.
0158
,.
53 + 2
×
.
0158] = [
.
498
,.
562]. The margin
of error is
.
0158
×
2 =
.
0316.
(2) Interpret the conﬁdence level of 95% (so that your roommate can understand you).
A: Suppose we repeatedly sample 1000 people, and calculate the interval, the interval will change
from time to time. In the long run, 95% of times the interval covers the true value of
p
.
Problem 2:
Continue from Problem 1. Suppose we want to test the hypotheses:
H
0
:
p
=
.
5
versus
H
1
:
p > .
5.
(1) Calculate the pvalue.
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 Winter '11
 Wu

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