A young researcher was evaluating a standard method for determining the methylme

Question

A young researcher was evaluating a standard method for determining the methylmercury content in blue fin tuna using high performance liquid chromatography (HPLC). She determined the standard deviation (s) for the method to be 0.53 ppb and assumed that s was a good approximation of . As a test, she used this method to evaluate the methylmercury content in a National Institutes of Standards and Technology (NIST) standard and determined the unknown amount to be within 0.24 ppb () of the known mean with 99% probability. How many replicate measurements of the NIST standard did the researcher perform?

Explanation / Answer

so here let say there are N replicate measurements of the NIST standard.

so the Margin of error here = 0.24 ppb

so margin of error = Test statistic * Standard erro of the mean

0.24 ppb = Z99% * (/ sqrt(N)

Z99% = 2.575

as = samle standard deviation = 0.53 ppb

=> 0.24 = 2.575 * (0.53/ sqrt(N)

sqrt(N) = 2.575 * 0.53/ 0.24

N = 32.335

so N = 33 measurements must have been taken.

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