If you have a choice, always compare against the population SD.
The sample SD is (usually) only a bad approximation of the population SD.
The story: healthy three year olds have a mean weight of 12.1515 and a standard deviation of 1.3448
I have a sample of children and I'm comparing it to the population of healthy babies.
the question im faced with is:
"How many standard errors (to the nearest hundredth) is the sample mean different from the expected mean for a healthy population (e.g. -4.34)"
sample 1 mean = 12.045 kg so the difference is |12.045-12.1515| and then that is divided by the standard error.
standard error is given by
(standard deviation)/sqrt(n) where n is the sample size.
So the question is which standard deviation do I use? the sample SD or the population SD?
my guess is that I should use the sample SD, but since we are comparing our sample to the population maybe measuring the distance in means using the population SD is best?