We know that in statistics all samples are different. I could take a sample of student GPAs, and Mrs. Cain could take a sample of student GPAs, and chances are that our mean GPA would not be exactly the same.
Since a confidence interval is created AROUND a sample parameter (x-bar or p-hat), and since all samples are different, all confidence intervals will then also be different. My 95% confidence interval will be different from Mrs. Cain's 95% confidence interval.
95% of the time, a 95% confidence interval will still capture the true population parameter. For example, if I took a sample and made a 95% confidence interval every day, 95% of the intervals that I make will have the true population mean in them. The other 5% won't - that's why we're only 95% confident that our interval is correct.
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