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A study is planned to estimate the mean concentration of a pollutant in stream s

ID: 3182320 • Letter: A

Question

A study is planned to estimate the mean concentration of a pollutant in stream sediments in a defined area at a given point in time. The sediments have been samples extensively in past years in this tame area, so the variability in the measurements is known to be s2 = 100 (ppm)2. We assume s2 /N is ~ 0, that is N is very large relative to s. Study objectives require that enough measurements be taken such that Var (x) will be no larger than V = 4 ppm2.

a. How many measurements are needed?

b. Suppose no prior data area available and that n1 = 15 data are collected and used to provide an estimate for s2, here calculated as s2 = 95. Now how many (additional) samples are required?

Explanation / Answer

a) sample size = (1/2) * [Z critical * s / margin error] 2

= (1/2) [3 * 10 / 4]2

= 28.125

b)

sample size = (1/2) * [Z critical * s / margin error] 2

= (1/2) [3 * 9.747 / 4]2

= 26.72

Approximately 27 samples required