Question: #13. Serving time. According to the Bureau of Crime Statistics and Research of Australia, as reported by the website www.agd.nsw.gov.au, the mean length of imprisonment for motor-vehicle theft offenders in Australia is 16.7 months. You want 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. Part B) The null and alternative hypotheses obtained are Ho: \(\mu \) = 16.7 months Ha: \(\mu \) not= 16.7 months where u is the mean length of imprisonment for motor vehicle theft offenders in Sydney, Australia. Explain what each outcome would mean:

(a) Type I error :

(b) Type II error:

(c) Correct decision.

(d) Then, suppose the results carrying out the hypothesis test would lead to nonrejection of the null hypothesis. Classify that conclusion by error type or as a correct decision if in fact the mean length of imprisonment for motor vehicle theft offenders in Sydney equals 16.7 months and then does not equal 16.7 months.