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 2037 riders not wearing a helmet. Complete parts ​(a) and ​(b) below.

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

a=0.05 level of significance. What are the null and alternative​ hypotheses?

Location of injury Multiple locations Head Neck Thorax Abdomen/ Lumbar/ Spine

Proportion 0.570 0.310 0.030 0.060 0.030

Location of injury and fatalities for 2037 riders not wearing a helmet

Location of injury Multiple locations Head Neck Thorax Abdomen/ Lumbar/ Spine Number

Proportion    1020 851 32 86 48

Answer 1

a)

Hypotheses are:

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

Ha:  The distribution of fatal injuries for riders not wearing a helmet do not follow the distribution for all​ riders.

Following is the calculations for chi square test statistics:

	O	p	E=2037*p	(O-E)^2/E
	1020	0.57	1161.09	17.14456941
	851	0.31	631.47	76.31941486
	32	0.03	61.11	13.8666683
	86	0.06	122.22	10.73382752
	48	0.03	61.11	2.812503682
Total	2037	1	2037	120.8769838

The test statistics is

(O-120.88

Degree of freedom: df=n-1=4

The p-value is: 0.0000

Since p-value is less than 0.05 so we reject the null hypothesis.