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

Answer 1

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