Use Chi Square Tables

#1
Based on a sample size of 80 I've calculated the CV% and Standard Deviation for a particular measurement. Those statistics represent a Marketing Specification. Now, I would like to make the same measurement, but only use 10 samples. Is there a way to calculate (95% confidence), perhaps using Chi Square Tables, what an acceptable %CV and Standard Deviation would now be using only 10 samples. In other words, if the CV% for the measurement was, say 2.0% using 80 samples, I imagine an acceptable CV% using 10 samples would be higher. But how much higher.
 

katxt

Active Member
#2
This doesn't look like a job for chi square tables which deal with counts, rather than measurements.
As I read it, you take a sample of 80 and calculate the CV to be 2%. That is the end of the "calibration". From then on you take samples of 10. You want to be able to say something like "So long as the CV is less than 3.1% we will accept this sample as being near enough to the calibration set."
For me, the easiest way to solve this problem is to do a simulation, though another reader may have an exact formula.
Assume the true CV to be 2%. Make the mean 100 then SD = 2. Make a sample of 10 normal numbers of mean 100, SD 2. Find the CV% of this sample. Write it down. Repeat many times (say 2000). Sort the results. Find the percentiles you want.
In this case a 95% CI is near enough between 1% and 3%. A one sided CI is < 2.8%.
This can be easily done in Excel.