In class today I had a bit of a discrepancy with my teacher.
I later found out that it means we have a different definition of probability when it comes to limited trial situations.
She believes the “probability” can only be 0 or 1, which is apparently the frequentist approach to statistics.
According to the google definition that is false.
On a test she would say
“There is a 95% probability that the interval from 107.8 to 116.2 contains μ”
was false
while I would say it was true
I am really trying to understand her reasoning.
What would happen if something like this came up on an AP FRQ?
I wouldn’t set this up as a conflict of Bayesian versus frequentists. You should understand what your teacher is trying to say: what is the probability that 3.14150 < 333/106 < 3.14151? That makes no sense to say that the probability is 0.6 or something, because even if you don’t know exactly what 333/106 is, it is still a constant. Just like \mu in your example.
Yes, Bayesians would interpret data differently and use the same words to mean different things. Don’t use that as an excuse not to understand what your teacher is telling you!
To answer your question, the AP stats curriculum, as far as I can tell, is frenquentist, and would count it as wrong if you say the probability that the population mean is between two constants is 95%.
my teacher, who has been teaching the course for a while, holds the same stance as OP’s teacher. The answer is false according to him.
so i would assume so
At the ap grading, answers are very specifically stated for the teachers grading. College board sets the standard and teachers are expected to follow it, so something like this probably wouldn’t show up.