Question

In: Statistics and Probability

A traffic safety company publishes reports about motorcycle fatalities and helmet use. In the first accompanying...

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.)

Solutions

Expert Solution

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.

orchestra answered 1 year ago
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