Estimate a Population Parameter

Estimation is a procedure by which a numerical value or values are assigned to a population parameter based on the information collected from a sample. The assignment of value(s) to a population parameter based on a value of the corresponding sample statistic is called estimation. In inferential statistics, _ is called the true population mean and p is called the true population proportion. There are many other population parameters, such as the median, mode, variance, and standard deviation.
The following are a few examples of estimation: an auto company may want to estimate the mean fuel consumption for a particular model of a car; a manager may want to estimate the average time taken by new employees to learn a job; the U. S. Census Bureau may want to find the mean housing expenditure per month incurred by households; and the AWAH (Association of Wives of Alcoholic Husbands) may want to find the proportion (or percentage) of all husbands who are alcoholic.
The examples about estimating the mean fuel consumption, estimating the average time taken to learn a job by new employees, and estimating the mean housing expenditure per month incurred by households are illustrations of estimating the true population mean. The example about estimating the proportion (or percentage) of all husbands who are alcoholic is an illustration of estimating the true population proportion, p.

This article explains how to assign values to population parameters based on the values of sample statistics. For example, to estimate the mean time taken to learn a certain job by new employees, the manager will take a sample of new employees and record the time taken by each of these employees to learn the job. Using this information, he or she will calculate the sample mean, then, based on the value of he or she will assign certain values to _.
As another example, to estimate the mean housing expenditure per month incurred by all households in the United States, the Census Bureau will take a sample of certain households, collect the information on the housing expenditure that each of these households incurs per month, and compute the value of the sample mean, Based on this value of the bureau will then assign values to the population mean, _. The sample statistic used to estimate a population parameter is called an estimator.
The estimation procedure involves the following steps. 1. Select a sample. 2. Collect the required information from the members of the sample. 3. Calculate the value of the sample statistic. 4. Assign value(s) to the corresponding population parameter. Remember, the procedures to be mentioned above assume that the sample taken is a simple random sample. If the sample is not a simple random sample, then the procedures to be used to estimate a population mean or proportion become more complex.