Question

The article “Leachate from Land Disposal Residential Construction

Waste” (authored by W.J. Weber, Y.-C Jang, T.G. Townsend, and S.

Laux, Journal of Environmental Engineering, 128 (3): 237 – 245, 2002)

presents a study on contamination at landfills containing construction and

demolition wastes. Specimens of leachate were taken from a test site. Out

of 42 specimens, 26 contained detectable levels of lead. 41 contained

detectable levels of arsenic, and 32 contained detectable levels of

chromium.

(a) Determine a 90% confidence interval for the probability that a

specimen will contain a detectable level of lead

(b) Determine a 95% confidence interval for the probability that a

specimen will contain a detectable level of arsenic.

(c) Determine a 99% confidence interval for the probability that a

specimen will contain a detectable level of chromium.

Answer 1

(a) Given : n=42 , X=26

The sample proportion , p=X/n=26/42=0.6190

q=1-p=0.3810

Therefore , the 90% confidence interval for the probability that a specimen will contains a detectable level of lead is ,

(b) Given : n=42 , X=41

The sample proportion , p=X/n=41/42=0.9762

q=1-p=0.0238

Therefore , the 95% confidence interval for the probability that a specimen will contains a detectable level of arsenic is ,

(c) Given : n=42 , X=32

The sample proportion , p=X/n=32/42=0.7619

q=1-p=0.2381

Therefore , the 99% confidence interval for the probability that a specimen will contains a detectable level of chromium is ,