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Statistical Inference: Estimation - Point and Interval Estimation

6 important questions on Statistical Inference: Estimation - Point and Interval Estimation

Which two types of estimations for a parameter are there?

Point estimation: a single number is the best estimation for a parameter value.
Interval estimation: an interval of numbers around the point estimate that contains the parameter value (called a confidence interval).

What is an estimator and what does it have to contain to be a good one?

An estimator describes a specific statistic to estimate something. A good estimator must have two qualities:

A sampling distribution that is centred around the parameter
A standard error as small as possible.

How do the estimator's sampling distributions look like when they are unbiased and when they are biased?

When an estimator's sampling distribution is unbiased, it is centred around the parameter.
When an estimator's sampling distribution is biased, it tends to under- or overestimate the parameter.

When would you call an estimator efficient?

An estimator is called efficient when it has a smaller standard error than other estimators.

What is a confidence interval?

A confidence interval for a parameter is an interval of numbers within which the parameter is believed to fall. The probability that this method produces an interval that contains the parameter is called the confidence level. This is a number chosen to be close to 1, such as 0.95 of 0.99.

What is the margin of error?

The margin of error is a multiple of the standard error (z-score x standard error). It can be used to determine the form of the confidence interval with the formula: point estimate ± margin of error.