Question

Perpetrators of a crime who have been given the maximum sentence of 10 years are believed by a fiscal to have been sentenced to more than 7 years on the average. A random sample of 20 of these crime offenders reveals a mean sentence of 7.6 years with a standard deviation of 2.4 years. Which of the following test statistic should be used?

Answer 1

$T=\sqrt{n}\frac{\bar{x}-\mu}{s}=\sqrt{20}\frac{7.6-7}{2.4}=1.11803\sim t_{n-1}=t_{19}\\One-tail\,\,test$