Here’s an easy error to fall into in statistics. Suppose I have n samples from a normal(μ, σ2) distribution, say n = 16, and σ is unknown. What is the distribution of the average of the samples? A common mistake is to say Student-t: if σ is known, the sample mean has a normal distribution, otherwise it has a t distribution.
But that’s wrong. Your ignorance of σ does not change the distribution of the data. There’s no spooky quantum effect that changes the data based on your knowledge. A linear combination of independent normal random variables is another normal random variable, so the sample mean has a normal distribution, whether or not you know its variance. Your knowledge or ignorance of σ doesn’t change the distribution of the data; it changes what you’re likely to want to do regarding the data. When the variance is unknown, you use procedures involving the sample variance rather than the distribution variance. This doesn’t change the distribution of the data but it changes the distribution you construct (implicitly) in your analysis of the data.