Task
9.77 Serving Time.
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 16.7 months.
One hundred randomly selected motor
vehicle-theft offenders in Sydney, Australia, had a mean length of imprisonment of 17.8 months.
At the 5% signicance level, do the data provide sufcient 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 6.0 months.
Answer :
Hypothesis test :
and6.7H0: μ = 1
= 6.7 (two tails) H1: μ / 1 → 2
α
.0σ = 6
0.05 .025α = → 2
α= 0
00n= 1
7.8x= 1
.83333333Zcalculated = x −μ
σ/√n=6/√100
17.8 −16.7 =0.6
1.1 = 1
.96Ztable = ± 1
ince z calculate in outside critical v alues,so f ailed to reject S H0
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.
Check with P -value test
values P(z.83333333) (1 (z.833333)) (1 0.96662222) .06675 P= 2 > 1 = 2 − P< 1 = 2 − = 0
0.05α =
Since > it means there is not enough evidence to conclude that the mean length of
values P α
imprisonment for motor-vehicle-theft offenders in Sydney differs from the national mean in
Australia.
