Solution to Homework 8 (STAT515, Fall 2011)
8.26
(
15 points
)
a.
The rejection region of a largesample lowertailed test at a signiﬁcance level of
α
= 0
.
01
is given by (
∞
,

z
0
.
01
)
≈
(
∞
,

2
.
33)
.
b.
z
=
¯
x

μ
0
s/
√
n
=
19
.
3

20
11
.
9
/
√
46
≈ 
0
.
40
.
c.
Notice that the value of the test statistic in part
b
does not fall in the rejection region
given in part
a
. Therefore, the observed data do not contradict with the statement under
H
0
strongly, thus we fail to reject
H
0
at 0.01 level of signiﬁcance. In summary, there is not
suﬃcient evidence from the sample to suggest that the true population mean number of latex
gloves used per week is below 20.
8.46
(
15 points
)
The summary statistics of the sample are,
n
= 11160 (large sample), ¯
x
= 2
.
15
,
and
s
= 1
.
05
.
The hypotheses are
H
0
:
μ
= 3 vs.
H
a
:
μ
6
= 3
.
a.
(
10 points
) The
p
value is given by
2
P
(
X
≤
2
.
15) = 2
P
±
X

3
1
.
05
/
√
11160
≤
2
.
15

3
1
.
05
/
√
11160
²
= 2
P
(
Z
≤ 
85
.
82)
≈
0
.
b.
(
5 points
) Because
p
value obtained in part
a
is less than
α
= 0
.
10
,
we reject
H
0
at
signiﬁcance level 0.10 and conclude that the mean level of aggressiveness for the population
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 Fall '10
 Zhao
 Statistics, Statistical hypothesis testing, rejection region

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