A researcher believes that perceptions about violent crime are related to the ty

Question

A researcher believes that perceptions about violent crime are related to the type of community where one was raised (rural, suburban, urban). A sample of 400 individuals is taken and it is found that 12.5% of the sample are from rural background, 50% are from a suburban background and 37.5% are from an urban background. Among those from a rural background, 20% believe violent crime is a significant and growing problem; 60% believe that is an important problem, but largely controlled; and 20% believe that is not a significant problem. Among those from a suburban background, 45% believe that violent crime is a significant and growing problem; 40% believe it is important, but controlled; and 15% believe that is not a significant problem. Finally, among those from an urban background, 40% believe violent crime is a significant and growing problem; 40% believe it is significant, but controlled; and 20% believe it is not significant. Based on this data, does it seem likely that there is a relationship between perceptions of violent crime and community background. Use the most appropriate hypothesis test we have learned with an ? = .01

Explanation / Answer

here we use chi-square test wtih

null hypothesis H0:there is no  relationship between perceptions of violent crime and community background

altenate hypothesi Ha: there is a relationship between perceptions of violent crime and community background

the test statistics chi-square=sum((O-E)2)/E=11.8 with (r-1)(c-1)=(3-1)(3-1)=4 df

critical chi-square(0.01,4)=13.3 is more than calcuated test statistic=11.8, so we fail to reject H0 and conclude that

there is no  relationship between perceptions of violent crime and community background.

following information has been generated using ms-excel

background significant important not significant rural 0.125 0.2 0.6 0.2 suburban 0.5 0.45 0.4 0.15 urban 0.375 0.4 0.4 0.2 background significant important not significant total rural 10 30 10 50 suburban 90 80 30 200 urban 60 60 30 150 total 160 170 70 400 observed(O) Expected(E) E (O-E) (O-E)2/E 10 50*160/400 20.0 -10.00 5 90 200*160/400 80.0 10.00 1.25 60 150*160/400 60.0 0.00 0 30 50*170/400 21.25 8.75 3.602941 80 200*170/400 85 -5.00 0.294118 60 150*170/400 63.75 -3.75 0.220588 10 50*70/400 8.75 1.25 0.178571 30 200*70/400 35 -5.00 0.714286 30 150*70/400 26.25 3.75 0.535714 sum 400 400.0 0.0 11.8

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