Question
According to the Bureau of Crime Statistics and Research of Australia, the mean length of imprisonment for motor-vehicle-theft offenders in Australia is 16.7 months. A
According to the Bureau of Crime Statistics and Research of Australia, the mean length of imprisonment
for motor-vehicle-theft offenders in Australia is 16.7 months. A group of researchers would like to perform
a hypothesis test to decide whether the mean length of imprisonment for motor-vehicle-theft offenders in
Sydney differs from the national mean in Australia. They have found out that Sydney population standard
deviation is 6.0. They have also decided to choose a random sample of size 100 and perform the test at the
significance level of 0.05. Suppose that, in reality, the mean length of imprisonment in Sydney is 15.5 months.
a. State the null and alternative hypotheses. (3 points)
b. Determine the probability of a Type I error.(2 points)
c. Determine the probability of a Type II error. (5 points)
d. Simulate 1,000 samples, each of size 100. (5 points)
e. Determine the mean of each sample in part (d). (5 points)
f. For the 1,000 samples obtained in part (d), about how many would you expect to lead to nonrejection
of the null hypothesis? Explain your answer. (5 points)
g. For the 1,000 samples obtained in part (d), determine the number that lead to nonrejection of the null
hypothesis. (5 points)
h. Compare your answers from parts (f) and (g), and comment on any observed difference. (5 points)
i. Plot the power curve for the range of true between 14 to 19. Interpret your plot. (5 points)
Step by Step Solution
There are 3 Steps involved in it
Step: 1
Get Instant Access to Expert-Tailored Solutions
See step-by-step solutions with expert insights and AI powered tools for academic success
Step: 2
Step: 3
Ace Your Homework with AI
Get the answers you need in no time with our AI-driven, step-by-step assistance
Get Started