Question

If a method produces a random error for each measurement of 4%, but a percent error of equal to or less than 1% is required for this value for later analysis, what is the minimum number of measurements that must be collected and averaged? You will need to solve equation 1 for the value of n that meets the criterion of a 1% error in the average.

Answer 1

Answer:

We need to take a sample of size n=16 to meet the criterion of a 1% error in the average.

Step-by-step explanation:

We have to calcuate the sample size that reduces 4 times the deviation of the measurement.

We can express that as the relation between the sampling distribution standard deviation and the population standard deviation. The last has to be 4 times the former:

$\sigma_s=\dfrac{\sigma}{4}$

We know that for a sampling distribution, the standard deviation is calculated as:

$\sigma_s=\dfrac{\sigma}{\sqrt{n}}$

Then, relating both equations, we have:

$\sqrt{n}=4\\\\n=4^2=16$

We need to take a sample of size n=16 to meet the criterion of a 1% error in the average.