Question

An engineer in the famous Continental tire manufacturer aims to investigate tire life for a new rubber compound. She has built 10 tires and tested them to end-of-life in a road test. The sample mean and standard deviation are 61550 and 3000 kilometers, respectively.

In order to perform hypothesis testing, state any necessary assumptions about the underlying distribution of the data.

Perform a seven-step procedure to investigate that the mean life of this new tire exceeds 60500km. Use α=0.05. (Hint: for alternative hypothesis, set parameter of interest be greater than 60500.)

c) Find the 95% lower confidence on the mean tire life

Use the confidence bound in part (c) to test the hypothes

Answer 1

To Test :-

H0 :- µ = 60500
H1 :- µ > 60500

One sided confidence interval
t(α, n-1) = t(0.05, 10- 1 ) = 1.833
61550 ± t(0.05, 10 -1) * 3000/√(10)
One sided lower bound = 61550 - t(0.05, 10 -1) 3000/√(10)
One sided lower bound = 59811.0635

95% lower confidence interval   ( - infinity , 59811.0635 )

Sice the value µ = 60500 does not lies in the lower bound, hence we fail to reject null hypothesis.

There is insufficient evience to support the claim that  mean life of this new tire exceeds 60500km.