Question: The County Prosecutor in Stanford County, Tom Smith believes that Judge Teresa Doe is, in a word, soft on crime. Old Tom is also thinking of running against Doe in the next election, so he is trying to decide if Judge Doe is really soft on crime. In Alabama the penalty for certain crimes is a minimum of 15 years in prison, and Tom thinks that Doe is sentencing convicts to less than those 15 years in the big house.

Tom pulls a random sample of 65 cases that Judge Doe has heard in the past 5 years and finds that the mean years in prison is 13.75 with a standard deviation of 3 years.

First, write the null and research hypotheses for this and then figure out if old Tom is correct or if Judge Doe has been following the sentencing rules.

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