409
Fall STAT 2009
Homework #5
(due Thursday, October 1, by 4:00 p.m.)
From the textbook:
6.6-2
6.6-4
6.6-8
6.6-10
6.7-2
6.7-4
6.7-12
6.7-18
6.8-12
if we believe the seed distributors claim;
b)
10.
a)
if we ignore the seed distributors claim.
Let X have a Binomial distribution with parameters n and p. Recall that
Xnp
n p (1 p )
has an approximate Standard Normal N ( 0, 1 ) provided distribution, that n is
large enough, and
P z 2 <
< z 2 1 .
n p (1 p )
Xnp
Show that an approximate 100 ( 1 ) % confidence interval for p is
p+
2
z 2
2n
z 2
1+
2
p ( 1 p ) z 2
+
n
4n2
,
2
z
where p =
2
X
n
.
n
This interval is called the Wilson interval. Note that for large n, this interval is
approximately equal to
p z
2
p (1 p )
.
n