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.