Question

A tire manufacturer claims that his tires have a mean life of 60,000 miles when used under normal driving conditions. A firm that requires a larger number of these tires wants to test the claim. If the claim is correct, the firm will purchase the manufacturer’s tires; otherwise, the firm will seek another supplier. Now a random sample of 100 tires is taken and the mean and standard deviation of the 100 tires are found. Using these sample results, a 95% confidence interval for the mean life of the tires is estimated as from 56,789 to 63,211 miles. The manufacturer’s claim is tested at the 5% significance level. Based on the given information, what should the firm do?

Select one:

a. Cannot be determined because of insufficient information.

b. The firm will seek another supplier.

c. The firm will purchase half from the manufacturer and the other half from another supplier.

d. The firm will purchase the manufacturer's tires.

Answer 1

Solution:

Claim: mean life of 60,000 miles

So , the null and alternative hypothesis are

H₀ : = 60000 vs H_a :    60000

Sample size = n = 100

95% confidence interval for the mean is (56789 , 63211 )

Hypothetical value 60000 is inside the interval (56789 , 63211 )

So ,

Fail to reject the null hypothesis H₀ : = 60000

Not sufficient evidence to reject the claim

So ,

d. The firm will purchase the manufacturer's tires.