STA406 Official Handouts

It is the procedure by which we reach a conclusion about a population on the basis of information contained in the sample drawn from that population. Two broad areas of statistical inference

•  Estimation
•  Hypothesis testing

Estimation

It is the process of calculating some statistics based upon the sample data drawn from a certain population. The statistics is used as an approximation to the population parameter.

Types of Estimate

For each of parameters, we can have

• Point Estimate

• Interval estimate

•  A point estimate is a single numerical value used to estimate the corresponding population parameter. Example: The mean of the age of men attending a show is 32 years.
•  An interval estimate consists of two numerical values defining a range of values that, with a specified degree of confidence, includes the parameter being estimated. Example: The mean of the age of men attending a show is between 28 and 36 years.

An estimator is defined to be unbiased if statistic used as an estimator has its expected value equal to the true value of the population parameter.

Suppose ˆ be an estimator of a parameter. Then ˆ will be

called an unbiased estimator if

said to be a biased estimator