Let's say I have a normal distribution of N ~ (1,0.01)
I pick 10 observations from that normal distribution. Is the confidence interval the same for 10 observations as it is for 100 observations? Or is there a difference?
If you really know the mean and the distribution of your data, no matter how much data you have, the mean distribution can be taken as if you had n as number of observations to infinity. Nevertheless, if you do not know the mean but you have only n data (As shown in the image below which is extracted from dummies.com), when the population standard deviation is known,
"the formula for a confidence interval (CI) for a population mean is"
Therefore, if you were to depend only on data, then the larger your n for an equal standard deviation, the smaller the confidence interval.