In: Statistics and Probability
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
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