An interval estimator is a type of estimator that calculates an interval of values for an unknown population parameter, meaning we calculate that the value of the population parameter is between the lower and upper bounds.
Types
Confidence Interval Estimator
Given a confidence level and a population parameter a confidence interval estimator provides an interval such that:
Calculation
Given a population parameter and an estimator , and a confidence level we can calculate the confidence interval as
where is the "critical value" which corresponds to the desired confidence level.
Critical Value
The critical value can be calculated in two ways depending on the survey used, for large sample sizes or where the population variance is known , where is the value of such that . Alternatively for small sample sizes with unknown population variance, .
Calculation for Mean
Given a survey of size , with a mean and a known population standard deviation we can calculate the confidence interval for as:
When the population standard deviation is unknown, we estimate it using the sample standard deviation. For a survey of size with a standard deviation , the confidence interval for the mean at confidence level is: