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 2051 riders not wearing a helmet. Using the data below, complete parts ​(a) and ​(b).

Location of Injury	Probability	Frequency
Multiple Locations	0.57	1025
Head	0.31	864
Neck	0.03	37
Thorax	0.06	80
Abdomen/Lumbar/Spine	0.03	45

(a) Compute the expected counts for each fatal injury.

Location of injury	Observed Count	Expected Count
Multiple Locations	1025	?
Head	864	?
Neck	37	?
Thorax	80	?
​Abdomen/Lumbar/Spine	45	?

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

(b) What is the P-value of the test? (round to three decimal places as needed)

Answer 1

(a)

Location of Injury	Observed count(O)	Expected count(E)
Multiple locations	1025	2051*0.57 = 1169.07	-144.07	20756.16	17.75
Head	864	2051*0.31 = 635.81	228.19	52070.68	81.9
Neck	37	2051*0.03 = 61.53	-24.53	601.72	9.78
Thorax	80	123.06	-43.06	1854.16	15.07
Abdomen/Lumbar/Spine	45	61.53	-16.53	273.24	4.44
Total	2051	2051			128.94

The chi square statistic = 128.94

and the degrees of freedom = (5 - 1) = 4

(b) The p value corresponding to chi-square statistic = 128.94 and df = 4 is 0.000

(From chi square table)