Answer: No, we do not have enough evidence to support the insurance company's claim.
Explanation:
Let
be the average car on the road .
As per given , we have
Null hypothesis :

Alternative hypothesis :

Since ,
is left-talied and population standard deviation is unknown , so we perform a left-tailed t-test.
Test statistic :
, where
= sample mean , s= sample standard deviation , n= sample size .
Put
= 5.8 years , s= 1.1 years , n= 15 .

Also, At 0.05 significance ,
(by t-distribution table)
Decision : Since
, so we fail to reject the null hypothesis .
Conclusion : At 5% confidence level , we do not have enough evidence to support the insurance company's claim.