1
The University of Hong Kong
Department of Statistics and Actuarial Science
STAT0302 Business Statistics
Semester 2 2009/2010
Example Class 8 Suggested Solution
1.
Let
X
be the weight of detergent packets (in grams) where
2
~
,
X
N
From calculator, we obtain
202.5
x
,
2.821620
s
and
14
n
.
(a)
An unbiased estimate for
is the sample mean
202.5
x
.
(b)
95% confidence interval for
is
1
2
. .
1
s
C I
x
t n
n
0.95
0.025
2.821620
. .
13
202.5
2.16
200.87,204.13
14
s
C I
x
t
n
where
0.025
13
t
is such that
0.025
13
0.025
P t
t
.
Look up
t
test Table, level of significance for twotailed tests= 0.05 (or level of
significance for onetailed tests= 0.025) and
13
df
. This gives
0.025
13
2.16
t
Interpretation: there is a 95 % chance that the true but unknown mean
falls in
the confidence interval
(c)
Setting up hypotheses:
0
:
204
H
v.s.
1
:
204
H
This is a twosided test.
The hypothetical value
0
204
lies inside the 95% confidence interval
This means that we do not reject
0
H
at
0.05
. There is no evidence to suggest
that
204
at the
0.05
level of significance.
Remarks: part (b) suggests that the true mean exceeds 204.13 with probability
0.025 and that it is lower than 200.87 with probability 0.025. In part (c), the
statistical test will reject the null hypothesis if the sample mean is either too large
or too small. If the sample mean is larger than
b
or is smaller than
a
, the null
hypothesis is rejected. These values
a
and
b
are specified by the significance
level. Given
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 Spring '09
 Prof.Chiu
 Statistics, Statistical hypothesis testing, brain tissue, test Table

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