In a study of 11,000 car crashes, it was found that 5720 of them occurred within 5 miles of home. Use a .05 significance level to test the claim that more than 50% of car crashes occur within 5 miles of home. Use our 4-step procedure.

Answer:Claim is trueStep-by-step explanation:n = 11000x = 5720Claim : 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]                                        =4.19Significance level = 0.05z at 0.05 = 1.64Since calculated z > defined zSo, null hypothesis is rejectedHence the claim is true that 50% of car crashes occur within 5 miles of home.