Homework
3
Solutions
8.12.
(a)
p
:
ffi
:0.4rir.
The
standard
enor
is
SEp
:
JiQ 
iW594:
0.008372,
so
the margin
of
error
for
95%
confi.dence
is
1.96SEi
:0.01641,
and
the interval
is
0.4007
to
0.4335.
(b)
The
margin
of
error
depends
on the confidence
level
(95Vo
in
both
cases) and
on
SEp.
The
sample
size
for
male
athletes
was
1.6
times larger
than
the
sample
for
female
athletes,
making the
males'
SEp smalier, resulting
in
a smaller margin
of
error
for
men.
(Another contributing
factor
to
the
smaller
SEp
for
males
was that
p(l

p)
was slightly
smaller
for
men: 0.2320 compared
to
0.2431for
women.)
8.1a.
(a)
The
standard
error is
SEp
:
^r/@39[0.3T1f1048
40.01429,
so
the margin
of
error
for
95Vo
confidence
is
1.96SEp:0.02800
and the
interval
is
0.6620
to
0.7180.
(b)
To
test
Ho:
p:0.79
vs.
f1o:
p
<0.79,
the
standard
error
is
op:
[email protected]\@2Tfffr48:0.01258
and
the test statistic
is
z
=
ffi*#
:
1
.95.
This
is
very
strong evidence against
I{s
(P
<
0.00005).
8,22,
(a)
Because
we
have
deflned
p
as
the proportion
who prefer
freshbrewed
coffee,
we
should
compute
p
:
#
:
0.J.To
test
Ho:
p:
0.5
vs.
Ho:
p>
0.5,
the
standard
error
is
o;
:
^/@$(0.5[40
:
0.0?906,
and the
test statistic
is
1
:
ffitH
=
2.53. The
p_
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 Spring '08
 Staff
 Normal Distribution, Standard Error

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