For n questions, we use the fact that N~Binomial(n, 0.25).
Since we were using the proportion of correct answers
/ ,
(
1)
E
(
)
,and
(
)
.
Instead, I incorrectly used E
(
) , (
)
(
1
),
whi
X Nn
pp
Xp
Va
rX
n
X
npVa
r
X
n
=

==
=
=
ch are actually for the Total # N of correct answers out of n questions.
0.3
5
0.25
If we use ,then
2.33,
0.25*0.75/
2.33
*
.1875
. .
,
or n = 101.79 (
n
102) to be 99% confident.
.10
However, if we use N
Xz
n
i
en

=≥
, then we need P(
N
.35n).
Approximating it by Normal distribution, ignoring continuity correction,
0.35n  0.25n
gives, z
=
2.33, i.e., same as above.
*0.25*0.75
Thus the answer for the incorrect problem
n
≤
=
actually gave the value of (1/n).
If we use the continuity correction,
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This note was uploaded on 04/16/2010 for the course STAT 427 taught by Professor Staff during the Spring '08 term at Ohio State.
 Spring '08
 Staff
 Binomial, Probability

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