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
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