In a study of 11000 car crashes it was found that 5720 of th

In a study of 11,000 car crashes, it was found that 5720 of them occurred within 5 miles of home. Use a 0.01 significance level to test the claim that more than 50% of car crashes occur within 5 miles of home.

1- What kind of test is this?

2-Where is the claim?

3-What is(are) the critical value(s)?

4-What is the test statistic and p-value?

5-What is your decision?

Select one: a. Reject the null hypothesis

b. Fail to reject the null hypothesis

and why

6-What is your conclusion?

Solution

a) test for a proportion

b) more than 50% of car crashes occur within 5 miles of home.

c) for alpha = 0.01

critical value : 2.32

p = 5720 / 11000 = 0.52

Z = 0.52 - 0.50 / srqt ( 0.50*0.50 / 11000 )

Z = 4.195

p value : 0.000005

decision

reject Ho

there is sufficient evidence to say that are more than 50% of car crashes occur within 5 miles of home.