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 2037 riders not wearing a helmet. Complete parts (a) and (b) below.
a) Does the distribution of fatal injuries for riders not wearing a helmet follow the distribution for all riders? Use
a=0.05 level of significance. What are the null and alternative hypotheses?
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 and fatalities for 2037 riders not wearing a helmet
Location of injury Multiple locations Head Neck Thorax Abdomen/ Lumbar/ Spine Number
Proportion 1020 851 32 86 48
a)
Hypotheses are:
H0: The distribution of fatal injuries for riders not wearing a helmet follow the distribution for all riders.
Ha: The distribution of fatal injuries for riders not wearing a helmet do not follow the distribution for all riders.
Following is the calculations for chi square test statistics:
O | p | E=2037*p | (O-E)^2/E | |
1020 | 0.57 | 1161.09 | 17.14456941 | |
851 | 0.31 | 631.47 | 76.31941486 | |
32 | 0.03 | 61.11 | 13.8666683 | |
86 | 0.06 | 122.22 | 10.73382752 | |
48 | 0.03 | 61.11 | 2.812503682 | |
Total | 2037 | 1 | 2037 | 120.8769838 |
The test statistics is
Degree of freedom: df=n-1=4
The p-value is: 0.0000
Since p-value is less than 0.05 so we reject the null hypothesis.
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