Probability vs Confidence
My notes on confidence give this question:
An investigator is interested in the amount of time internet users spend watching TV a week. He assumes hours and samples users and takes the sample mean to estimate the population mean .
Since is large we know that approximates the Standard Normal. So, with probability , the maximum error of estimate is hours.
The investigator collects that data and obtain hours. Can he still assert with 99% probability that the error is at most 1.27 hours?
With the answer that:
No he cannot, because the probability describes the method/estimator, not the result. We say that "we conclude with 99% confidence that the error does not exceed 1.27 hours."
I am confused. What is this difference between probability and confidence? Is it related to confidence intervals? Is there an intuitive explanation for the difference?