Question

Approximately 52% of all fatal auto accidents are caused by driver error, according to the American Automobile Association. 36 randomly selected fatal accidents are examined, and it is determined that 15 were caused by driver error. Using α = 0.10, is the AAA proportion accurate?

Answer 1

Solution :

Given that ,

n = 36

x = 15

The null and alternative hypothesis is ,

H0 : p = 0.52

Ha : p 0.52

This is the two tailed test .

= x / n = 15 / 36 = 0.4167

P0 = 52% = 0.52

1 - P0 = 1 - 0.52 = 0.48

Test statistic = z

= - P0 / [P0 * (1 - P0 ) / n]

= 0.4167 - 0.52 / [0.52 ( 1 - 0.52 ) / 36 ]

= -1.241

The test statistic = -1.241

P-value = 0.2146

= 0.10

0.2146 > 0.10

P-value >  

Fail to reject the null hypothesis .

There is not sufficient evidence to test the claim .