Conclusion: Since
p
-value > 0.05, we do not reject
0
H
. There is
insufficient evidence, at 5% level of significance, to conclude
that
22000
.
Example 8.10 :
The security department of a factory wants to know whether or not the true average time required by
the night guard to walk his round is 30 minutes. If, in a random sample of 100 rounds, the night guard
averaged 30.8 minutes with a standard deviation of 3.8 minutes, determine the minimum value of the
level of significance to claim that the true average time is not 30 minutes?
Solution :
Unbiased estimates for population mean and population variance,
2
2
100
sample variance
99
100
=
30.8
14.5
3
8
.8
59
9
1
9
3.819
x
s
s
Let
X
be the time required by the night guard to walk his round.
To test
0
1
:
30
:
30
H
H
at
% level of significance
Test Statistics: Under
0
H
, by Central Limit Theorem,
2
3.8191
~ N
30,
approximately
100
X
and test statistic,
2
100
~ N(0,1)
3.8191
100
X
Z

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