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 2051  riders not wearing a helmet. Complete parts (a) and (b) below.

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 Multiple locations  Head Neck Thorax Abdomen/ Lumbar/ Spine

Number 1029 857 36 82 47

a) Does the distribution of fatal injuries for riders not wearing a helmet follow the distribution for all​ riders? Use a = 0.01 level of significance. What are the null and alternative​hypotheses?

A. 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.

B. 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.

C. None of these.

Location of Injury         Observed Count    Expected Count

Multiple Locations 1029 ?

Head 857 ?

Neck 36   ?

Thorax 82 ?

Abdomen/lumbar/                  47                          ?

    spine

                        (round to 2 decimal places as needed)

What is the p value of the test?

P value = __ (Round to 3 decimal places as needed)

Based on the​ results, does the distribution of fatal injuries for riders not wearing a helmet follow the distribution for all other riders at a significance level of a = 0.01?

A. Do not reject Upper H 0. There is sufficient evidence that the distribution of fatal injuries for riders not wearing a helmet follows the distribution for all riders.

B. Reject Upper H 0. There is sufficient evidence that the distribution of fatal injuries for riders not wearing a helmet does not follow the distribution for all riders.

C. Reject Upper H 0. There is not sufficient evidence that the distribution of fatal injuries for riders not wearing a helmet follows the distribution for all riders.

D. Do not reject Upper H 0. There is not sufficient evidence that the distribution of fatal injuries for riders not wearing a helmet does not follow the distribution for all riders

(b) Compare the observed and expected counts for each category. What does this information tell​ you?

A. Motorcycle fatalities from head injuries occur less frequently for riders not wearing a helmet.

B. Motorcycle fatalities from head injuries occur more frequently for riders not wearing a helmet.

C. Motorcycle fatalities from thorax injuries occur more frequently for riders not wearing a helmet

  

Solutions

Expert Solution

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.

option A

Reject Upper H 0. There is sufficient evidence that the distribution of fatal injuries for riders not wearing a helmet does not follow the distribution for all riders.

OPTION B IS CORRECT

b) By comparing and observational counts

HEAD = 635.8/857 = 0.74

NECK = 36/61.5 =0.585

Motorcycle fatalities from head injuries occur more frequently for riders not wearing a helmet.

OPTION B IS CORRECT

orchestra answered 1 year ago
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