Question

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 1

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.

$H_0:p=0.5\\H_a:p>0.5$

We will use one sample proportion test  

$\widehat{p}=\frac{x}{n}\\\widehat{p}=\frac{5720}{11000}\\\widehat{p}=0.52$

Formula of test statistic =$\frac{\widehat{p}-p}{\sqrt{\frac{p(1-p)}{n}}}$

                                       =$\frac{0.52-0.5}{\sqrt{\frac{0.5(1-0.5)}{11000}}}$

                                       =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.