Answer:
Claim is true
Step-by-step explanation:
n = 11000
x = 5720
Claim : more than 50% of car crashes occur within 5 miles of home.
[tex]H_0:p=0.5\\H_a:p>0.5[/tex]
We will use one sample proportion test
[tex]\widehat{p}=\frac{x}{n}\\\widehat{p}=\frac{5720}{11000}\\\widehat{p}=0.52[/tex]
Formula of test statistic =[tex]\frac{\widehat{p}-p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
=[tex]\frac{0.52-0.5}{\sqrt{\frac{0.5(1-0.5)}{11000}}}[/tex]
=4.19
Significance level = 0.05
z at 0.05 = 1.64
Since calculated z > defined z
So, null hypothesis is rejected
Hence the claim is true that 50% of car crashes occur within 5 miles of home.
