Question

records for 14 cities of similar size and Socio-Econimic conditions were examined. unt of violent crimes in each city are shown for the year 2010. In 1960, 50 years Theer each of the cities accounted for the proportion of violent crimes shown in the table. eart tese results to test the claim that the cities account for the same proportions of crimes use 2010 as they did in 1960. Then answer the questions at the end of this problem. TObserved Proportion Hypotheses Cityin 2010 in 1960 S2 Ho 0.075 0.094 0.036 0.090 0.109 0.078 0.041 0.108 0.027 0.099 0.027 0.086 0.031 0.099 145 Ht Tails 100 126 347 Value of t 12 13 14 Symbolic test statisitc 398 4279 Conclusion Critical Region Picture Do Not Reject Ho Conclusion in terms of original Which observed value (City and count) had the greatest effect on the value of the Test Statistic (example: City #10, count-469)? What was the contribution to the test statistic value?

Answer 1

hypothesis

The following null and alternative hypotheses need to be tested:

Ha​: Some of the population proportions differ from the values stated in the null hypothesis

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alpha=0.05

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right tail

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symbolic test statistic

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value of test stat

Categories	Observed	Expected	(fo-fe)2/fe
Category 1	344	4279*0.075=320.925	(344-320.925)2/320.925 = 1.659
Category 2	437	4279*0.094=402.226	(437-402.226)2/402.226 = 3.006
Category 3	145	4279*0.036=154.044	(145-154.044)2/154.044 = 0.531
Category 4	416	4279*0.090=385.11	(416-385.11)2/385.11 = 2.478
Category 5	464	4279*0.109=466.411	(464-466.411)2/466.411 = 0.012
Category 6	320	4279*0.078=333.762	(320-333.762)2/333.762 = 0.567
Category 7	160	4279*0.041=175.439	(160-175.439)2/175.439 = 1.359
Category 8	444	4279*0.108=462.132	(444-462.132)2/462.132 = 0.711
Category 9	100	4279*0.027=115.533	(100-115.533)2/115.533 = 2.088
Category 10	469	4279*0.099=423.621	(469-423.621)2/423.621 = 4.861
Category 11	126	4279*0.027=115.533	(126-115.533)2/115.533 = 0.948
Category 12	347	4279*0.086=367.994	(347-367.994)2/367.994 = 1.198
Category 13	109	4279*0.031=132.649	(109-132.649)2/132.649 = 4.216
Category 14	398	4279*0.099=423.621	(398-423.621)2/423.621 = 1.55
Sum =	4279	4279	25.185

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critical region

Based on the information provided, the significance level is α=0.05, the number of degrees of freedom is df = 14 - 1 = 13, so then the rejection region for this test is R={χ2:χ2>22.362}

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Since it is observed that χ2=25.185>χc2​=22.362, it is then concluded that the null hypothesis is rejected.

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conclusion:there is enough evidence to reject the claim that cities account for same proportion of crimes in 2010 as they in 1960

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city 10 count 469 has greatest effect on the value of chi square

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contibution of city 10 to test statistic is 4.861