Judge Robert Smith is accused of being “soft on crime,” especially in cases involving white collar crimes like fraud and embezzlement. The judge has responded to the accusation by insisting that the average sentence he has handed out in such cases is more severe than that for any other judge in the region. In fact, he claims the average sentence he has handed down in these cases is at least 80 months. You take a simple random sample of 36 of the judge’s white collar cases (from the total population of white collar cases presided over by the judge during the past ten years) and find that the average sentence in these cases is 72 months. Set up an appropriate hypothesis test. Assume the standard deviation for the population of Judge Smith’s white collar cases is 18 months.
a. Show the null and alternative hypotheses.
b. State the appropriate decision rule using a significance level of 2%.
c. Compute the sample test statistic, z stat.
d. Should the null hypothesis be rejected? Explain.