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
records for 14 cities of similar size and Socio-Econimic conditions were examined. unt of violent crimes...