Destructive sampling, in which the test to determine whether an item is defective destroys the item, is generally expensive, and the high costs involved often prohibit large sample sizes. For example, suppose the National Highway Traffic Safety Administration (NHTSA) wishes to determine the proportion of new tires that will fail when subjected to hard braking at a speed of 60 miles per hour. NHTSA can obtain the tires for $25 (wholesale price) each. Suppose the budget for the experiment is $10,000, and NHTSA wishes to estimate the percentage that will fail to within 0.02 with 95% confidence. Assuming that the entire $10,000 can be spent on tires (ignoring other costs), and that the true fraction that will fail is approximately .05, can NHTSA attain its goal while staying within the budget? Explain.