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In: Statistics and Probability

Are births equally likely in each month of the year? Perform a complete test of hypothesis...

Are births equally likely in each month of the year? Perform a complete test of hypothesis using the data below from 2006. Please show calculator or excel steps used. Total: 4,265,555 January: 340,297 Feburary: 319,235 March: 356,786 April: 329,809 May: 355,437 June: 358,251 July: 367,934 August: 387,798 September: 374,711 October: 367,354 November: 351,832 December: 356,111

Solutions

Expert Solution

Ho: births are equally likely in each month of the year

H1: births are not equally likely in each month of the year

chi square goodness of fit test

observed ,O expected proportion expected ,E (O-E)²/E
jan 340297 0.083 355463 647.058
feb 319235 0.083 355463 3692.261
mar 356786 0.083 355463 4.925
apr 329809 0.083 355463 1851.455
may 355437 0.083 355463 0.002
jun 358251 0.083 355463 21.868
jul 367934 0.083 355463 437.536
aug 387798 0.083 355463 2941.397
sep 374711 0.083 355463 1042.271
oct 367354 0.083 355463 397.785
nov 351832 0.083 355463 37.088
dec 356111 0.083 355463 1.182
total 4265555 4265555 11074.828

chi square stat = Σ(O-E)²/E = 11074.828

df = 12-1 = 11

p-value=0.000 [excel function: =CHISQ.DIST.RT(11074.828,11)

since, p-value <α=0.05, reject Ho

hence, births are not equally likely in each month of the year at α=0.05

orchestra answered 3 years ago
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