Question

Use an example to illustrate the difference between parameter, estimator, and estimate.

Answer 1

Sol

Population is descriptive measure that describes a population

An estimator of a population parameter is a random variable that depends on sample information whose value provides an approximation to this unknown parameter

that is sample statistics used to estimate a population parameter is called as estimator

A specific value that obtained from a sample to estimate a population parameter

Suppose we have sample of 6 observation 2,3,4,5,6

parameter here is population mean represented by mu

estimator of population mean is sample mean denoted by xbar

estimate is xbar=sum of values//total values

=2+3+4+5+6/5

=20/5

=4

Example:

Internet sites report that about 13% of Americans are left handed.During a exam , the instructor walks around the room and counts 15 left handed students out of 98 in the class

Here

parameter is population proportion=p=13%=0.13

estimator is sample proportion= p^=x/n

estimate is p^=15/98=0.15306