Chapter 6.2, Problem 4Q

Company records show that drivers get an average of 32,500 miles on a set of Road Hugger All-Weather radial tires. Hoping to improve that figure, the company has added a new polymer to the rubber that should help protect the tires from deterioration caused by extreme temperatures. Fifteen drivers who tested the new tires have reported getting an average of 33,800 miles. Can the company claim that the polymer has produced a statistically significant increase in tire mileage? Test $H_0:\mu =32,500$ against a one-sided alternative at the $\alpha =0.05$ level. Assume that the standard deviation $\left(\sigma \right)$ of the tire mileages has not been affected by the addition of the polymer and is still four thousand miles.