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 purchase the manufacturer's tires.

c. The firm will seek another supplier.

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

Answer 1

Answer:-

We wants to test

Null hypothesis ( H0) : < 60,000 miles. Vs. Alternative hypothesis (H1). : = 60,000 miles

To use a confidence interval, simply make the following observations: If our confidence interval contains the value claimed by the null hypothesis, then our sample result is close enough to the claimed value, and we therefore do not reject H0.

Since our 95% confidence interval for the mean life of the tires is lies between 56,789 to 63,211 miles contains the value claimed by null hypothesis. Hence we do not reject H0 .

That is,

The firm will speak the another supplier.

Hence, option (c) is correct.