Map Sapling Learning macmillan learning When choosing the sample size needed for

Question

Map Sapling Learning macmillan learning When choosing the sample size needed for an experiment to reduce the sampling variance for a single analysis to a desired level, the sampling constant, Ks, can be used. The formula is where m is the sample mass and R is the relative standard deviation A certain analysis method was determined to have a sampling constant of Ks is required for a sampling standard deviation of ±3.0%? 31 g. What mass of sample Number How many samples of this size must be analyzed in order to give 90% confidence that the mean is known to within 2.0%? Number Enter your answer samplesas a whole number.

Explanation / Answer

a) Given R = 3.5 (RSD is expressed as a percentage) and KS = 25 g, plug in values and get

mR2 = KS

====> m*(3.5)2 = (25 g)

====> m = (25 g)/(3.5)2 = 2.0408 g 2.041 g.

Therefore, the mass of the sample required is 2.041 g (ans).

b) The margin of error is 2.2%.

Use the relation

margin of error = Z*(RSD)/n where n is the number of samples analysed.

Z* = 1.645 at 90% CL.

Plug in values

2.2 = 1.645*(3.5)/n

====> n = 2.6170

===> n = 6.8489 7

Therefore, 7 replicates measurements must be made (ans).

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