Surfstat.australia: an online text in introductory Statistics

STATISTICAL INFERENCE

POINT ESTIMATION AND INTERVAL ESTIMATION

In any estimation problem, we need to obtain both a point estimate and an interval estimate. The point estimate is our best guess of the true value of the parameter, while the interval estimate gives a measure of accuracy of that point estimate by providing an interval that contains plausible values.

Sample Mean

When the variable of interest is quantitative, the sample mean provides a point estimate of the unknown population mean. When the variable has a binomial distribution, the sample proportion is a point estimate of the unknown population proportion p.

Confidence Interval

Confidence interval are frequently used as interval estimates. Articles in the research literature commonly report 95% confidence intervals (95% CI). The 95% CI is calculated in such a way that under repeated sampling it will contain the true population parameter 95% of the time. The figure 95% is a measure of the confidence you have that the interval contains the true population parameter. Confidence intervals may be computed for any level of confidence: 90% or 99% confidence intervals are sometimes used. We will examine this topic in more detail after a brief overview of some results from probability theory which are useful.


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