Statistics • Estimation of the Mean and Proportion
A point estimate is a single best-guess value for a population parameter, such as xbar for mu or p-hat for p. An interval estimate is a confidence interval that gives a range of plausible values around the point estimate.
It uses the template estimate +/- (critical value) x (standard error). The critical value comes from the selected confidence level, and the standard error depends on whether you are estimating a mean or a proportion.
Use a z interval when the population standard deviation sigma is known. Use a t interval when sigma is unknown and you use the sample standard deviation s, with degrees of freedom df = n - 1.
The normal-approximation interval works best with random or independent sampling and a sample size that is not too small. In practice, the method is most reliable when both n x p-hat and n x (1 - p-hat) are reasonably large.
A 95% confidence level means that if the same method were repeated on many random samples, about 95% of the resulting intervals would contain the true parameter. It does not mean there is a 95% probability that a single computed interval contains the true value.