1. The U.S. Environmental Protection Agency (EPA) defines the Action Level for l
ID: 3075427 • Letter: 1
Question
1. The U.S. Environmental Protection Agency (EPA) defines the Action Level for lead in tap water as 15 parts per billion (ppb; 15 ppb 0.015 mg/l). This is a level above which further analysis and public education campaigns must be done, but not yet a level causing a real health risk. A random sample of 10,341 water specimens from the Washington DC area found that 7,496 water specimens had lead contents up to 15 ppb. (a) (6pts) Estimate the true proportion of all possible water specimens in DC that have lead contents up to 15 ppb? Use a 95% confidence interval. Be sure to show work and provide an interpretation of your interval! (b) (4 pts) What sample size would be required to have a margin of error within .01 of a 99% confidence interval for the true proportion of all possible water speciments in DC that have lead contents up to 15 ppb?Explanation / Answer
a)
X = 7496
n = 10341
95 % confidence interval
(p^ - z * sqrt(pq/n) , p^ + z * sqrt(pq/n))
p^ = X/n = 7496/10341 = 0.72488
z = 1.96
hence confidence interval is (0.716274, 0.733489)
b)
n = z^2 *pq/e^2
= 2.576^2 * 0.72488 * (1-0.72488)/0.01^2
= 13233.6607635
=13234
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