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 no more than 7 years on 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. Is the fiscal correct in his suspicions at 0.05 level of significance?

Answer 1

$\mu=7 \\ n=20 \\ \bar{x}=7.6 \\ s=2.4 \\ α=0.05 \\ H_0: \mu=7 \\ H_1: \mu > 7 \\ df=n-1 = 20-1=19$

Test statistic:

$t= \frac{\bar{x}- \mu}{s / \sqrt{n}} \\ = \frac{7.6-7}{2.4 / \sqrt{20} } \\ = \frac{0.6}{0.5366} \\ = 1.118$

Read the t-table value at 5% level of significance at 19 degrees of freedom for Right tailed test is 1.72

t-cal<t-tab

So, we accept H₀ and reject H₁.

We can conclude, that the fiscal is correct in his suspicions at 0.05 level of significance.