Bulletproof Vests. In the 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. (See page 556 for the details of this procedure.) c. Explain the large discrepancy between the two methods. d. Which confidence interval would you use? Explain your answer.
Bulletproof Vests. In the 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. (See page 556 for the details of this procedure.)
c. Explain the large discrepancy between the two methods.
d. Which confidence interval would you use? Explain your answer.
Given,
a.One-proportion z-interval procedure
As per z-distribution table, the z-critical value at 95% confidence level is obtained as 1.96 i.e. zα/2=1.96
The required confidence interval by one-proportion z-interval procedure is obtained as follows:
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