An insurance company claims the average car on the road is less than 6 years old. Based on a random sample of 15 cars, the mean age is 5.8 years with a standard deviation of 1.1 years. Does the sample support the insurance company's claim?

No, we do not have enough evidence to  support the insurance company's claim.

Step-by-step 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.