Question

The Acme Tire Company has been sued by a class of vehicle owners who experienced tire failure on cars manufactured by the Speedy Motor Company during the second quarter of 2005. The cars were relatively new, having between 1,500 and 2,800 miles traveled. The car owners filed claims on the tire warrant and Acme rejected the claims after finding that the damage and failure was the result of significant over inflation.

Acme Tire requires that their tires not be inflated in excess of 38.5 psi. Further, the purchase agreement between Acme Tire and Speedy Motor Company requires that cars leaving the assembly plant have less than 3% of the tires over inflated. Acme Tire Company has data from a random sample of tire inflation pressures from vehicles manufactured by Speedy during the second quarter of 2005 with the following characteristics:

Sample Size 126 tires

Number Over inflated 16

You have been hired by Acme Tire’s in house legal department to provide advice as they consider whether or not to file suit against Speedy Motor Company for failure to meet the over inflation restriction in the tire purchase agreement. Prepare a report for the legal department regarding the implications of the results of the sample. Compute, cite and discuss confidence intervals of 90%, 95%, and 99% the population proportion of over inflated tires and their resultant sampling errors.

A few months later, in an effort to assure the problem did not recur, Speedy Motor and Acme Tire agreed to work together to monitor tire inflation on assembled vehicles. Since you were so knowledgeable and helpful, they have asked you to suggest a sampling program to determine the following on a monthly basis:

- Proportion of over inflated tires with a sampling error of 0.03, CI of 95% (The over inflated proportion of the population is assumed to be 6%, with a population standard deviation of 0.5)

If it will cost about $5 per sampled tire, how much more would it cost to increase the CI to 99% for both the estimate of the proportion?

Answer 1