Title: Confidence Intervals and the Normal Distribution | Statistical Analysis with Excel 2010: Using Excel with the Normal Distribution | InformIT
Headings: Statistical Analysis with Excel 2010: Using Excel with the Normal Distribution
Statistical Analysis with Excel 2010: Using Excel with the Normal Distribution
This chapter is from the book
Confidence Intervals and the Normal Distribution
The Meaning of a Confidence Interval
Constructing a Confidence Interval
Excel Worksheet Functions That Calculate Confidence Intervals
Using CONFIDENCE.NORM () and CONFIDENCE ()
Using CONFIDENCE.T ()
Using the Data Analysis Add-in for Confidence Intervals
Confidence Intervals and Hypothesis Testing
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Content: Does that tell you that the true population mean is somewhere between 45 and 55? No, it doesn't, although it might well be. Just as there are many possible samples that you might have taken, but didn't, there are many possible confidence intervals you might have constructed around the sample means, but couldn't. As you'll see, you construct your confidence interval in such a way that if you took many more means and put confidence intervals around them, 95% of the confidence intervals would capture the true population mean. As to the specific confidence interval that you did construct, the probability that the true population mean falls within the interval is either 1 or 0: either the interval captures the mean or it doesn't. However, it is more rational to assume that the one confidence interval that you took is one of the 95% that capture the population mean than to assume it doesn't. So you would tend to believe, with 95% confidence, that the interval is one of those that captures the population mean. Although I've spoken of 95% confidence intervals in this section, you can also construct 90% or 99% confidence intervals, or any other degree of confidence that makes sense to you in a particular situation. You'll see next how your choices when you construct the interval affect the nature of the interval itself.