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Task
9
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According to the Bureau of Crime Statistics and Research of Australia, as reported on Lawlink,
the mean length of imprisonment for motor-vehicle-theft offenders in Australia is 16
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One hundred randomly selected motor
vehicle-theft offenders in Sydney, Australia, had a mean length of imprisonment of 17
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At the 5% signicance level, do the data provide sufcient evidence to conclude that the mean
length of imprisonment for motor-vehicle-theft offenders in Sydney differs from the national
mean in Australia? Assume that the population standard deviation of the lengths of
imprisonment for motor-vehicle-theft offenders in Sydney is 6
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Answer :
Hypothesis test :
H 0 : μ = 16
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7 (two tails) →
σ = 6
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05 → 2α = 0
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8

Z calculated =

x −μ
σ/√n

=

17
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7
6/√100

=

1
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6

= 1
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96
S ince z calculate in outside critical values, so f ailed to reject H 0
Conclusion
So, there is not enough evidence to conclude that the mean length of imprisonment for
motor-vehicle-theft offenders in Sydney differs from the national mean in Australia
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83333333) = 2(1 − P (z < 1
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96662222) = 0
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05

Since P values > α it means​ ​there is not enough evidence to conclude that the mean length of
imprisonment for motor-vehicle-theft offenders in Sydney differs from the national mean in
Australia

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