Question

The mean concentration of cadmium in 6 contaminated soil samples was found to be 0.875 with a standard deviation of 0.134. If it is desired to know the mean with a precision of 2% (RSD), how many additional samples must be taken?

Answer 1

Answer on Question #65163 – Math – Statistics and Probability

Question

The mean concentration of cadmium in 6 contaminated soil samples was found to be 0.875 with a standard deviation of 0.134. If it is desired to know the mean with a precision of 2% (RSD), how many additional samples must be taken?

Solution

$$ME = z_{crit} \frac{s}{\sqrt{n}} \rightarrow n = \left(\frac{z_{crit} s}{ME}\right)^2 = \left(\frac{1.96 * 0.134}{0.02}\right)^2 = 173.$$

Number of additional samples is

$$n = 173 - 6 = 167.$$

Answer: 167.

Reference:

[1] Clay, K. (2017, February 9). How to determine sample size, determining sample size. Retrieved February 9, 2017, from https://www.isixsigma.com/tools-templates/sampling-data/how-determine-sample-size-determining-sample-size/

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