Question

2) The results of a random sample of 531 persons injured in bicycle crashes are summarized in the table below. At the 0.05 significance level, test the claim that that bicycle helmet use is independent of the type of injuries are received in a crash. Facial injuries received All injuries non-facial Helmet Worn 30 83 No Helmet Worn 182 236 (a) State the null and alternative hypothesis. (b) Find and label the observed frequencies and the expected frequencies. (c) The test statistic is x² = 10.69. Perform the test and state the specific conclusion for this problem.

Answer 1

a).hypothesis:-

b). the observed and expected table be:-

		helmet worn	helmet not worn	row total
facial injuries received	oberved	30	182	212
	expected	(113*212)/531 = 45.11	(418*212)/531 = 166.89
all injuries non-facial	observed	83	236	319
	expected	(113*319)/531 = 67.89	(418*319)/531 = 251.11
	column total	113	418	531

c). test statistic is :-

$\chi^2=10.69$

df = (2-1)*(2-1) = 1

p value = 0.0011

[ in any blank cell of excel type =CHISQ.DIST.RT(10.69,1) ]

decision:-

p value = 0.0011< 0.05 (alpha)

we reject the null hypothesis. There is not sufficient evidence to claim that helmet use is independent of type of injuries received.

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