What about situations in which there is no prior information? Even here the interpretation is complex. The problem is that there can be more than one procedure that produces intervals that contain the population parameter 95% of the time. Which procedure produces the "true" 95% confidence interval? although the various methods are equal from a purely mathematical point of view, the standard method of computing confidence intervals has two desirable properties: (1) each interval is symmetric about the point estimate and (2) each interval is contiguous. Recall from the introductory section in the chapter on probability that for some purposes, probability is best thought of as subjective. It is reasonable, although not required by the laws of probability, that one adopt a subjective probability of 0.95 that a 95% confidence interval as typically computed contains the parameter in question.

Confidence intervals can be constructed for any estimated parameter, not just μ. For example, one might estimate the proportion of people who could pass a training program or the difference between the mean for subjects taking a drug and those taking a placebo. Click below for details:

Mean, σ known

Mean, σ

Difference between means, σ known

Difference between means, σ estimated

Pearson's correlation

Difference between correlations

Proportion

Difference between proportions