1. The manufacturer of the X-15 steel-belted radial truck tire claims that the mean mileage the tire can be driven before the tread wears out is 65,000 miles. Assume the mileage wear follows the normal distribution and the standard deviation of the distribution is 5,000 miles. Crosset Truck Company bought 48 tires and found that the mean mileage for its trucks is 59,000 miles. Is Crosset's experience different from that claimed by the manufacturer at the .05 significance level? Apply 5-step process for hypothesis testing and make a decision.
2. Transmission EX Company manufactures truck transmissions. The weekly production of the Model EX-25 follows a normal probability distribution with a mean of 250 and a standard deviation of 22. Economic recovery and higher sales of trucks requires boost in output of the plant and therefore more advanced assembly machinery has been installed. The head of manufacturing would like to know if her ideas has paid off and the mean of daily production is different from 250 at the .01 significance level? Follow the 5-step hypothesis testing and show your decision.