Question

A traffic safety company publishes reports about motorcycle fatalities and helmet use. In the first accompanying data​ table, the distribution shows the proportion of fatalities by location of injury for motorcycle accidents. The second data table shows the location of injury and fatalities for 2068 riders not wearing a helmet.

Location of Injury   Probability   Frequency
Multiple Locations   0.570   1027
Head   0.310   869
Neck   0.030   40
Thorax   0.060   83
Abdomen/Lumbar/Spine   0.030   49

​(a) Does the distribution of fatal injuries for riders not wearing a helmet follow the distribution for all​ riders? Use

alphaαequals=0.050.05

level of significance. What are the null and alternative​ hypotheses?

A.

H0​: The distribution of fatal injuries for riders not wearing a helmet does not follow the same distribution for all other riders.

H1​: The distribution of fatal injuries for riders not wearing a helmet does follow the same distribution for all other riders.

B.

H0​: The distribution of fatal injuries for riders not wearing a helmet follows the same distribution for all other riders.

H1​: The distribution of fatal injuries for riders not wearing a helmet does not follow the same distribution for all other riders. Your answer is correct.

C.

None of these.

Compute the expected counts for each fatal injury.

Location of injury	Observed Count	Expected Count
Multiple Locations	1027	__?__
Head	869	__?__
Neck	40	__?__
Thorax	83	__?__
​Abdomen/Lumbar/Spine	49	__?__

​(Round to two decimal places as​ needed.)

Answer 1

a)

The null and alternative hypothesis is

B.

H0​: The distribution of fatal injuries for riders not wearing a helmet follows the same distribution for all other riders.

H1​: The distribution of fatal injuries for riders not wearing a helmet does not follow the same distribution for all other riders.

Level of significance = 0.05

Expected count = n*pi

n = 2068

Location of injury	Observed Count	Expected Count
Multiple Locations	1027	1178.76
Head	869	641.08
Neck	40	62.04
Thorax	83	124.08
Abdomen/Lumbar/Spine	49	62.04

Test statistic is

O: Observed frequency
E: Expected frequency.

	O	p	E	(O-E)	(O-E)^2	(O-E)^2/E
	1027	0.57	1178.76	-151.76	23031.1	19.53841
	869	0.31	641.08	227.92	51947.53	81.03127
	40	0.03	62.04	-22.04	485.7616	7.829813
	83	0.06	124.08	-41.08	1687.566	13.60063
	49	0.03	62.04	-13.04	170.0416	2.740838
Total	2068				Total	124.741

Degrees of freedom = Number of E's - 1 = 5 - 1 = 4

Critical value = 9.488

( From chi-square critical value table)

Test statistic > critical value we reject null hypothesis.

Conclusion: The distribution of fatal injuries for riders not wearing a helmet does not follow the same distribution for all other riders.