Answer :
Answer:
There is sufficient evidence to support the claim that the fatality rate is higher for those not wearing seat belts.
Step-by-step explanation:
Among 2823 occupants not wearing seat belts, 31 were killed.
[tex]y_1=31\\n_1=2823[/tex]
Among 7765 occupants wearing seat belts, 16 were killed.
[tex]y_2=16\\n_2=7765[/tex]
Let [tex]p_1[/tex]and [tex]p_2[/tex] be the fatality rate for hose not wearing seat belts and wearing seat belts receptively .
Claim :the fatality rate is higher for those not wearing seat belts
So, [tex]H_0:p_1=p_2[/tex]
[tex]H_a:p_1> p_2[/tex]
We will use Comparing Two Proportions
[tex]\widehat{p_1}=\frac{y_1}{n_1}[/tex]
[tex]\widehat{p_1}=\frac{31}{2823}[/tex]
[tex]\widehat{p_1}=0.01098[/tex]
[tex]\widehat{p_2}=\frac{y_2}{n_2}[/tex]
[tex]\widehat{p_2}=\frac{16}{7765}[/tex]
[tex]\widehat{p_2}=0.00206[/tex]
[tex]\widehat{p}=\frac{y_1+y_2}{n_1+n_2}=\frac{31+16}{2823+7765} =0.00443[/tex]
Formula of test statistic : [tex]\frac{\widehat{p_1}-\widehat{p_2}}{\sqrt{\widehat{p}(1-\widehat{p})(\frac{1}{n_1}+\frac{1}{n_2})}}[/tex]
Test statistic : [tex]\frac{0.01098-0.00206}{\sqrt{0.00443(1-0.00443)(\frac{1}{2823}+\frac{1}{7765})}}[/tex]
Test statistic : [tex]\frac{0.01098-0.00206}{\sqrt{0.00443(1-0.00443)(\frac{1}{2823}+\frac{1}{7765})}}[/tex]
Test statistic : [tex]6.111[/tex]
Significance level- 0.05
So, z at 0.05 = 1.96
z statistic > z critical
So, We failed to accept null hypothesis
Hence There is sufficient evidence to support the claim that the fatality rate is higher for those not wearing seat belts.
