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. 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 = 0.10 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

  

Answer 1

a) 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.

Category	Observed (O)	Proportion, p	Expected Frequency (E)	(O-E)²/E
1	1029	0.57	2051 * 0.57 = 1169.07	(1029 - 1169.07)²/1169.07 = 16.7822
2	857	0.31	2051 * 0.31 = 635.81	(857 - 635.81)²/635.81 = 76.9491
3	36	0.03	2051 * 0.03 = 61.53	(36 - 61.53)²/61.53 = 10.5929
4	82	0.06	2051 * 0.06 = 123.06	(82 - 123.06)²/123.06 = 13.7
5	47	0.03	2051 * 0.03 = 61.53	(47 - 61.53)²/61.53 = 3.4312
Total	2051	1.00	2051	121.4554

Test statistic:

χ² = ∑ ((O-E)²/E) = 121.46

df = n-1 = 4

p-value = CHISQ.DIST.RT(121.4554, 4) = 0.00

Conclusion:

B. Reject H0. There is sufficient evidence that the distribution of fatal injuries for riders not wearing a helmet does not follow the distribution for all riders.

b)

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