alright dickheads let's see what you can do
Explain to me in a convincing way why a 95% CI does not mean a 95% probability that one will draw a random sample with the population mean in it
>>8592242
The real question is, why WOULD it mean that? Please explain what chain of logic lead you to this odd confusion.
a CI of 95% means that if the null hypothhesis is true then 95% of the time a randomly drawn sample will have a sample mean in that interval.
So I can't explain to you why it is not the case because it IS the case
>>8592251
If I have a sack of marbles with 95% white and 5%black marbles in them, there is a .95 probability that a random marble i will draw eill be a white one, right?
So if we have an infinite pool of samples, and we can say that 95% of these samples lie within a certain range of the population mean, why can't I say that a randomly drawn sample has a 95% chance to be within that range?
>>8592278
Because once you've drawn a sample, there's no randomness left in that sample. The randomness comes from drawing the sample. Once that is done, you have no randomness and you can just calculate the mean to determine whether the population mean is in the range. There's no probability here. It's like saying a constant is probabilistic, which it really isn't.
>>8592278
How do you calculate mean and confidence intervals with a categorical problem? (I.e. black or white). What is the mean of 4 black and 5 white marbles? How does a black marble lie within a range of the mean? What does that even mean?????