In the New York Times article “A Common Police Vest Fails the Bulletproof Test,” E. Lichtblau reported on a U.S. Department of Justice study of 103 bulletproof vests containing a fiber known as Zylon. In ballistics tests, only 4 of these vests produced acceptable safety outcomes (and resulted in immediate changes in federal safety guidelines). Find a 95% confidence interval for the proportion of all such vests that would produce acceptable safety outcomes by using the
a. One-proportion z-interval procedure.
b. One-proportion plus-four z-interval procedure.
c. Explain the large discrepancy between the two methods.
d. Which confidence interval would you use? Explain your answer.