Question

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?

Answer 1

To Test :-

H0 :- µ >= 6
H1 :- µ < 6

Test Statistic :-
t = ( X̅ - µ ) / (S / √(n) )
t = ( 5.8 - 6 ) / ( 1.1 / √(15) )
t = -0.7042

Test Criteria :-
Reject null hypothesis if t < -t(α, n-1)
Critical value t(α, n-1) = t(0.05 , 15-1) = 1.761
t > -t(α, n-1) = -0.7042 > - 1.761
Result :- Fail to reject null hypothesis

Decision based on P value
P - value = P ( t > 0.7042 ) = 0.2464
Reject null hypothesis if P value < α = 0.05 level of significance
P - value = 0.2464 > 0.05 ,hence we fail to reject null hypothesis
Conclusion :- Fail to reject null hypothesis

There is insufficient evidence to support the claim that the average car on the road is less than 6 years old.