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

Claim is true

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}=(x)/(n)\\\widehat{p}=(5720)/(11000)\\\widehat{p}=0.52`

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

=
`\frac{0.52-0.5}{\sqrt{(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.