Question

A particular report from 2004 classified 721 fatal bicycle accidents according to the month in which the accident occurred, resulting in the accompanying table.

Month	Number of Month Accidents
January	37
February	33
March	44
April	60
May	78
June	73
July	97
August	85
September	63
October	67
November	43
December	41

(a) Use the given data to test the null hypothesis H₀: ?₁ = 1/12, ?₂ = 1/12, . . . , ?₁₂ = 1/12, where ?₁ is the proportion of fatal bicycle accidents that occur in January, ?₂ is the proportion for February, and so on. Use a significance level of 0.01. (Use 2 decimal places.)
?² =  

(b) The null hypothesis in Part (a) specifies that fatal accidents were equally likely to occur in any of the 12 months. But not all months have the same number of days. Test the hypotheses proposed in H₀: ?₄ = ?₆ = ?₉ = ?₁₁ =

30

366

? 0.082, ?₂ =

29

366

? 0.079, ?₁ = ?₃ = ?₅ = ?₇ = ?₈ = ?₁₀ = ?₁₂ =

31

366

? 0.085 using a 0.05 significance level. (Use 2 decimal places.)
?² =  

Answer 1

(a) =sum(O-E)²/E=78.37 with k-1=12-1=11 df

critical chi-square(0.05,11)=19.67 is less than calucted chi-square, so we reject null hypothesis and conclude that each months are not equal

Month	Oberved(O)	Expected(E)	(O-E)	(O-E)2/E
January	37	60.08333333	-23.0833	8.868354
February	33	60.08333333	-27.0833	12.20816
March	44	60.08333333	-16.0833	4.305247
April	60	60.08333333	-0.08333	0.000116
May	78	60.08333333	17.91667	5.342695
June	73	60.08333333	12.91667	2.776815
July	97	60.08333333	36.91667	22.6825
August	85	60.08333333	24.91667	10.33299
September	63	60.08333333	2.916667	0.141586
October	67	60.08333333	6.916667	0.796232
November	43	60.08333333	-17.0833	4.857258
December	41	60.08333333	-19.0833	6.061142
total	721	721	-2.8E-14	78.37309

(b) =sum(O-E)²/E=7.81417with k-1=4-1=3 df

critical chi-square(0.05,3)=7.8147 is more tthan calucted chi-square, so we accept null hypothesis and conclude that each months are equal

Month	Oberved(O)	Expected(E)	(O-E)	(O-E)2/E
April	60	59.75	0.25	0.001046
June	73	59.75	13.25	2.938285
September	63	59.75	3.25	0.176778
November	43	59.75	-16.75	4.695607
total	239	239	0	7.811715

(c)chi-square=52.89 with k-1=7-1=6 df

critical chi-square(0.05,6)=12.59 is less than calucted chi-square, so we reject null hypothesis and conclude that all months is not equal

Month	Oberved(O)	Expected(E)	(O-E)	(O-E)2/E
January	37	64.14285714	-27.1429	11.48584
March	44	64.14285714	-20.1429	6.325485
May	78	64.14285714	13.85714	2.993637
July	97	64.14285714	32.85714	16.83105
August	85	64.14285714	20.85714	6.782055
October	67	64.14285714	2.857143	0.127267
December	41	64.14285714	-23.1429	8.349984
total	449			52.89532