3. What is point estimation?

ANS. Inferential statistics are used to determine the likelihood that a conclusion, based

on the analysis of the data from a sample, is true and represents the population studied.

The 2 common forms of statistical inference are:

• Estimation

• Null hypothesis tests of significance

There are two forms of estimation.

1. Point estimation

2. Interval estimation

Both estimation and null hypothesis tests of significance are used to infer parameters. (A

parameter is a statistical constant that describes a feature about a phenomena,

population etc.)

POINT ESTIMATION:

Point estimates are single points that are used to infer parameters directly. For example,

• Sample proportion P˄ (“p hat”) is the point estimator of p

• Sample mean X (“x bar”) is the point estimator of µ

• Sample standard deviation SD is the point estimator of Ϭ

OBJECTIVE: The objective of the point estimation is to calculate the sample

observations, as single number that is likely to be close to the unknown value of the

parameter.

A statistical intended for estimating a parameter is called a point estimator. The standard

deviation of this estimator is called its standard error or S E.

The estimation of the parameters of a statistical model is one of the fundamental issues in

statistics. Choosing an appropriate estimator, that is “best” in one or another aspect, is an

important task.

Let X1 ,X,2,X3…..Xn denote the observations in a random sample of size n from a population.

Let µ, population mean and population standard deviation can be denoted by respectively.

The sample mean Xˉ = Point estimator of µ. The sample standard deviation SD,S is a point

estimator of Ϭ. The SD of Xˉ is called its standard error and is given by Ϭ/√n.

By the central limit theorem, is approximately normal with mean=µ and SD=Ϭ/√n.

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Note that the standard error of Xˉ depends on the sample size, n the larger the sample size,

the smaller is the SD, indicating that the sampling variability will be smaller for larger

samples.

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