#### Estimation :

It is the procedure by which we estimate the unknown value of the population parameter by using the sample observation.

There are two types of estimation :

- Point Estimation
- Interval Estimation

Estimation in statistics |

**Point Estimation :**

The process of finding single value as an estimate of an unknown parameter by using simple observation is called point estimation.

**Interval Estimation **:

The procedure in which we estimate the range of values with the parameter is expect to lie with some probability of confidence that interval contain the parameter is called interval estimation.

**Estimate** :

A single numerical value obtain from sample of observation to represent the unknown parameter to estimate. It is also called point estimate. For example:

Suppose we wish to estimate the average age of first year college students.We select a random sample of one hundred students and their average age comes out to be 16 year is the point estimate.

**Define Estimator :**

It is the rule or formula which is used to estimate the value of population parameter by using sample observation is called estimator. E.g ** x̄ = Σx /n**

#### Internal Estimate :

An interval of values obtain from sample observation with in which the parameter lies under probability of confidence is called interval estimate.

E. g.

Suppose we want to estimate the average marks of one hundred students.If average mark is x̄=70 then it will be point estimate but if we find that We are 98% confident that means lies between 65 to 80 then it is called interval estimate.

**Testing of Hypothesis :**

It is a process which enable us to take decisions about the unknown value of population parameter.On the basis of sample observation at alpha level of significance.In it, we either accept or reject the statement about parameter.

**Null Hypothesis :**

The hyperthesis which we wish to test is called Null hypothesis.

It is denoted by **Ho.A**nd it is tested for the purpose of possible rejection. It always contain the sign of equality.

For example:

If we stat that the average age of first year student is a 16 year then is the null hypothesis.

**Alternative Hypothesis :**

The hypothesis which is opposite from the null hypothesis and which is automatically accepted when the null hypothesis is rejected is called alternative hypothesis.

It is denoted by H1.

For example:

If null hypothesis then alternative hypothesis may be

a) H1:H**≠**16

b) H1:H>16

C) H1:H<16

Level of significance:

The probability of making a type one error is called level of significance.

it is denoted by alpha.

Type 1 error if we reject null hypothesis when is really true then there is an error called type 1 error or alpha error.

A good player is not allow to play match.

An intelligent student is not promoted to next class.

Type 2 error if we accept null hypothesis when is false then there is an error called type 2 error.

It is also called beta error.

For example:

The coach selected an untrain person player. The teacher recomended a weak students for scholarship.

Test statistic:

A test statistic is a function or formula of sample observation that provides a basis for testing a null hypothesis.The most commonly used test statistics are the Z, t and F.

Rejection region:

The value of the statistic which leads to reject the null hypothesis is called rejection region or critical region.

It is only denoted by Alpha.

Acceptance:

The value of test statistic which leads to a accept the null hypothesis is called the acceptance region.

It is denoted by 1 minus Alpha.

Sample Distribution:

The procedure of selecting a sample from given population is called sampling.

Sampling frame:

A complete list of all the sampling unit is called sampling frame.Sampling frame is a list, a map or any other material which guides us to cover the whole population.

**Sampling design:**

A plan for obtaining a sample from a given population is called sample design of sampling design. A simple design is always specified before any data are collected.

**Sample with replacement:**

If a sampling unit is drown from population and is returns from the population before the next selection then this procedure is called sampling with replacement.Inthis case the size of population does not change and the probability of selection for every unit remain same. In this case,a unit may be selected more than once.

**Sampling without replacement:**

If the selected sample unit is not returned to the population before the next selection then this precedure is called sampling without replacement. In this case, the size of population will be reduced after every selection.So the probability of selection for each unit will be different.In this case,a unit is selected only once.

**Probability Sampling:**

The process in which the selection of unit from population depend upon the chance is called probability sampling. The probability of selection for every unit may be equal or unequal but it should be known it has three type.

Simple random sampling.

Stratified random sampling

Systematic sampling

Non Probability Sampling:

Non probability sampling the selection is not based on chance. Somebody may use his personal judgement on experience for the selection of sample.It also called non-random sampling.