Question: Engineers at a tire manufacturing corporation wish to test a new tire material for increased durability. To test the tires under realistic road conditions, new front tires are mounted on each of 11 company cars, one tire made with a production material and the other with the experimental material. After a fixed period the 11 pairs were measured for wear. The amount of wear for each tire (in mm) is shown in the table:
a. Give a point estimate for the difference in mean wear.
b. Construct the 99% confidence interval for the difference based on these data.
c. Test, at the 1% level of significance, the hypothesis that the mean wear with the experimental material is less than that for the production material.