In: Statistics and Probability
Over a 20-year period, the average sentence given to defendants convicted of aggravated assault in the United States was 25.9 months. Assume this to be your population mean. Because you think it might be different in your home state, you conduct a little study to examine this question. You take a random sample of 175 jurisdictions in your home state and find that the mean sentence for aggravated assault is 27.3 months, with a standard deviation of 6.5. Test the null hypothesis that the mean sentence length in your state is 25.9 months against the alternative hypothesis that it is different from that. Set your alpha level at .01.
given data are:-
sample mean () = 27.3
sample sd (s)= 6.5
sample size(n) = 175
level of significance () = 0.01
here,as the population sd is unknown i am doing 1 sample t test for mean.
hypothesis:-
test statistic be:-
df = (n-1)= (175-1) =174
p value = 0.0049
[ in any blank cell of excel type =T.DIST.2T(2.8493,174) press enter ]
decision:-
p value = 0.0049 < 0.01(alpha)
so, we reject the null hypothesis.
conclusion:-
there is sufficient evidence to support the claim that the mean sentence length in your state is different 25.9 months at 0.01 level of significance.
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