i need some clarification here. i have the following in my notes:
1) Confidence interval is a type of interval estimate that gives a range of values in which a population statistics might lie
2) 95% confidence interval does NOT mean that the probability of our population mean lying in the interval is 95%
3) 95% confidence interval means that if we calculated the 95% confidence interval for 100 samples, about 95 of these would contain the true population mean
I’m having a hard time distinguishing #2 and #3. For #3, doesn’t that mean that if we took 100 samples and calculated a confidence interval for each, if I randomly chose one of those confidence intervals, then there is a 95% chance that my population mean lies in this interval?
Or in other words, for #3, another way to say it is if I took an increasing number of samples, let’s say 100,000 samples and calculated each confidence interval, then roughly 95,000 of those CI will contain the population mean. Which sounds like if I have a random sample and calculate its confidence interval, then there is a 95% chance that it contains the population mean
Are any of my definitions/notes off? I’m sure my logic is faulty here. Thanks!