As you can tell, there are several ways to obtain a confidence interval for a process probability. When the sample size is large, they will yield very similar results for the endpoints and the coverage rate. When the sample size is small, the Adjusted Wald method is preferred. You can use the
Clopper-Pearson confidence interval method when the sample size is small, but the Binomial intervals tend to be wider and don’t have the estimate ± margin-of-error simplicity, and is much more computational efficient than the Blaker method.
Whatever procedure is used to determine the confidence interval, you interpret a (valid) interval the same way – as the interval of plausible values for the parameter. For example, we are 95% confident that the underlying probability of death within 30 days of a heart transplant operation at St. George’s Hospital is between 0.16 and 0.24; where by “95% confident,” we mean that if we were to use this procedure to construct intervals from thousands of representative samples, roughly 95% of those intervals will succeed in capturing the actual (but unknown) value of the parameter of interest.
Keep in Mind: The main things you should focus on in your study of confidence intervals are:
• What parameter is the interval estimating (in context)?
• What are the effects of sample size, confidence level, and the sample statistic on the width and midpoint of the interval?
• What do we mean by “confidence”?
• What are the effects (if any!) of sample size, confidence level, and the actual parameter value on the coverage rate of the method?
• Why might one confidence interval method be preferred over another?
Also note how to use technology to perform these calculations. You should NOT use the Simulating Confidence Intervals applet to construct a confidence interval for a particular sample of data.