Question

AAA claims that over 54% of fatal car/truck accidents are caused by driver error, a researcher studied 30 randomly selected accidents and found that 14 were caused by driver error. test the AAA claim at a level of significance of a=0.10

H0

H1

CV

Test Statistic

Answer 1

Since we have to test if the number of accidents caused by driver error is equal to 54%, this is a two tailed test as there is no direction specified (greater than or lesser than).

The Hypothesis:

H0: p = 0.54

Ha: p 0.54

This is a 2 Tailed Test.

The Test Statistic: = 14 / 30 = 0.467

The Critical Value:   The critical value (2 tail) at = 0.10, Z critical = -1.645 and +1.645

The Decision Rule: If Z observed is > Z critical or if Z observed is < -Z critical, Then Reject H0.

The Decision: Since Z lies in between -1.645 and +1.645, We Fail To Reject H0

The Conclusion: There isn't sufficient evidence at the 90% significance level to warrant rejection of the claim by the AAA that the percentage of accidents caused by driver error is equal to 54%.