d). the confidence level c represents the proportion of all (fixed) intervals that would contain the parameter if we repeated the process many, many times.
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I'm having trouble understanding this question: Discuss the statements in the context of what we actually mean by a confidence interval. a). Once the endpoints of the confidence interval are numerically fixed, then the parameter in question (either mu or p) does or does not fall inside the "fixed" interval.
B). A given fixed interval either does or does not contain the parameter mu or p; therefore the probablity is 1 or 0 that the parameter is in the interval.
C). Nontrival probability statements can be made only about variables, not constants.
This might be too lateto help, but here goes cuz I love this stuff!
Think of the confidence interval as a net of a fixed size trying to capture the true (and unknowable) mu. Statement D is saying that if a net is made with these numeric methods and swung a bazillion times, we can expect 80% (for example) of the swings to catch the true mu.
Statement A is saying that once we set the size of the net and swing, we either caught the true mu or we didn't. (We have no way of knowing if it's in there.)
Statement B is another way of saying Statement A. If we caught mu, there is a 100% chance that it's in the net If we missed it, there is 0 probability that it is in the net. (But we have no way of knowing if it's in or out.)
I think Statement C is saying something similar to Statement B. To switch images, let's say you roll a 5 with a die. What is the probability that it is a 5? 100% !!! What is the probability that it is not a 5? 0%. Only unknowns have probabilities worth discussing. BEFORE you roll, you have a 1/6 chance of getting a 5. Once you have rolled, the only options are 100% or 0%.