Question

To study the amount of jail time (in years) served by convicted murderers in Manitoba and Ontario, samples were taken by both provinces. Province Sample Size Sample Mean Sample Standard Deviation Manitoba 10 12.4 2.72 Ontario 12 13.8 2.63 a) (6 points) Test using the 10% significance level whether there is a significant difference in the mean jail time between the two provinces. b) (2 points) State the assumption(s) required for the test.

Answer 1

let manitoba is sample 1 so

n1=10 m1=12.4 S1=2.72

ontario is sample 2 so

n2=12 m2=13.8 S2=2.63

a)

we have to test that

HO : μι - μ2 = 0, H, :μι - μ2 40

test statistics is given by

ml – m2 12.4 – 13.8 t -1.22 S12 + S22 n2 V n1 2.722 10 + 2.632 12

t will have df =min{(n1-1),(n2-1)} =min{9,11}=9

now P value =P(t<-1.22) =0.1267

since P Value is more than level of significance (0.1) Hence we failed to reject H0 Hence we do not have enough evidence to conlcude that two means are different.

b)

assumptions: both populations are normal

variance of two populations are un equal.