ANLT 202

Assignment 1: Hypothesis Test (40 points)

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)