I am trying to calculate the survey sample size necessary to estimate average rice yield.
If the standard deviation is 10 tons, then the variance is 100. Plugging this into the sample size formula (at 95% confidence, 5% MoE, 100,000 population) then I need a sample of 16.
But, if I change the unit of measurement to kg, the same standard deviation is 10000kg. The variance then becomes 100,000,000. The required sample size skyrockets to 99,354.
Why should changing the units of the variable change the required sample size? Does this mean that I can get around any sample size problems by simply changing the units of measurement? Apologies if this is too simple a question for this forum, but I've hunted far and wide on the internet for the intuition behind this...