A traffic safety company publishes reports about motorcycle fatalities and helme

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 2071 riders not wearing a helmet. Complete parts (a) and (b) below Help Me View an Click the icon to view the tables Textbool StatCrur (a) Does the distribution of fatal injuries for riders not wearing a helmet follow the distribution for all riders? Use alternative hypotheses? at are the null and 0.10 level of significance. What are the null and H0: The distribution of fatal injuries for riders not wearing a helmet does not follow the same distribution for all other riders H: The distribution of fatal injuries for riders not wearing a helmet does follow the same distribution for all other riders. A. Tech Hel B. Ho: The distribution of fatal injuries for riders not wearing a helmet follows the same distribution for all other riders. Ask My H: The distribution of fatal injuries for riders not wearing a helmet does not follow the same distribution for all other riders Print OC. None of these Distribution of fatalities by location of injury mpute the expected counts for each fatal njury. Full data set Location of injury Observed CountExpected Count Proportion of fatalities by location of injury for motorcycle accidents Multiple Locations Head ec Thorax Abdomen/Lumbar/Spine 1021 880 40 82 48 Multiple locations Abdomen/ Location of injury Thorax Lumbar/ Spine Head Neck Pr on 0.570 0.310 0.030 0.060 0.030 Location of injury and fatalities for 2071 riders not wearing a helmet Multiple locations 1021 Abdomen/ Location of injury Thorax Lumbar/ Spine Head Neck (Round to two decimal places as needed.) Number 880 40 82 48 Enter your answer in the edit fields, then click Check Answer. Print Done 3 parts remaining

Explanation / Answer

We simply multiply the proportions by 2071 to get the expected values.

Doing an observed/expected value table,          

[ANSWER]

*********************************************************

Using chi^2 = Sum[(O - E)^2/E],          
          
chi^2 =    135.2329193 [ANSWER, TEST STATISTIC]
          
As df = a - 1,           
          
a =    5      
df = a - 1 =    4      
          
Then, the critical chi^2 value is          
          
significance level =    0.05      
chi^2(crit) =    9.487729037      
          
Also, the p value is          
          
p =    2.95783*10^-28 [ANSWER, P VALUE]
          
Thus, as P < 0.10, we   REJECT THE NULL HYPOTHESIS.      

There is sigificant evidence that the distribution of riders without helmet is different from the distribution of those with helmet. [CONCLUSION]

          
Thus, there is significant evidence that there is a difference that the variables are dependent to each other.          

Observed Expected (O - E)^2/E 1021 1180.47 21.54284 880 642.01 88.22174 40 62.13 7.882455 82 124.26 14.37235 48 62.13 3.213535

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