10.51
Let
p
1
and
p
2
denote the probability of survival for the treated group (with
carbolic acid) and the control group (without carbolic acid), respectively.
We
formulate the hypotheses:
versus
.
The test statistic is
.
Since
H
1
is twosided and
, the
rejection region is
(illustrated below).
ffddb18f5169bd51dc4679f2ce66163f8ea7b21b
13
We calculate the following:
Pooled estimate
,
Observed
z
is
,
which lies in
R
.
Hence,
H
0
is rejected at
.
Furthermore, the associated
p

value.
This means that
H
0
would be
rejected with
as small as 0.0036.
As such, a difference in the survival rates
is strongly demonstrated by the data.
10.52
Estimated S.E. =
So, a 95% confidence interval for
is given by
()
or (0.11, 0.51).
10.55
(a) Let
p
1
and
p
2
denote the probability of having prominent wrinkles for
smokers and nonsmokers, respectively. We
formulate the hypotheses:
versus
.
The test statistic is
.
Since
H
1
is rightsided, the rejection
region is of the form
.
We calculate the following:
ffddb18f5169bd51dc4679f2ce66163f8ea7b21b
14
Pooled estimate
,
Observed
z
is
The associated
p
value is is less than 0.0002.
So, there is very strong evidence in
support of
H
1
.
(b) A direct causal relation between smoking and wrinkled skin cannot be readily
concluded.
Various psychophysiological factors could influence both the
smoking habit and the presence of wrinkled skin.
10.58
(a) We formulate the hypotheses:
versus
.
The test statistic is
, where we identify
as
, respectively.
Since
H
1
is rightsided and
, the rejection
region is .
We calculate the following:
Pooled estimate
,
Observed
z
is
,
which does not lie in
R
.
Hence,
H
0
is not rejected at
.
(b) We formulate the hypotheses:
versus
.
The test statistic is
, where we identify
as
, respectively.
Since
H
1
is rightsided, the rejection region is of
the form
.
We calculate the following:
ffddb18f5169bd51dc4679f2ce66163f8ea7b21b
15
Pooled estimate
,
Observed
z
is
The associated
p
value is less than 0.0002.
Hence, the data strongly
substantiate
H
1
.
Answer Keys
Chapter 11
11.1
The points on the line
for
and
are (1,5) and (4,14)
respectively.
The intercept is 2 and the slope is 3.
ffddb18f5169bd51dc4679f2ce66163f8ea7b21b
16
11.2 (a)
If
, then
.
(b)
We must determine the smallest
x
value such that
.
Solving this inequality yields .
So, we must sell at least 16 batteries in a month
in order to make a profit.
11.3 (a)
Predictor variable
x
= duration of training
Response variable
y
= performance in skilled job
(b)
Predictor variable
x
= average number of cigarettes smoked daily
Response variable
y
= CO level in blood
(c)
Predictor variable
x
= Humidity level in environment
Response variable
y
= Growth rate of fungus
(d)
Predictor variable
x
= Expenditures in promoting product
Response variable
y
= Amount of product sales
11.10
(a) At ,
.
At 6
x
=,
.
(b) No, only the mean is larger.
By chance the error
e
at , which has standard
deviation 3, could be quite negative and/or the error at
very large.
11.11
(a) At ,
.
At 5
x
=,
.
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 Spring '08
 NAUS
 Statistics, Normal Distribution, Variance, Statistical hypothesis testing