# Statistical Inference: An Introduction

### Introduction to Statistical Inference

Inference means conclusion. When we discuss statistical inference, it is the branch of Statistics that deals with the methods to make conclusions (inferences) about a population (called reference population or target population), based on sample information. The statistical inference is also known as inferential statistics. As we know, there are two branches of Statistics: descriptive and inferential.

Statistical inference is a cornerstone of many fields of life. It allows the researchers to make informed decisions based on data, even when they can not study the entire population of interest. The statistical inference has two fields of study:

### Estimation

Estimation is the procedure by which we obtain an estimate of the true but unknown value of a population parameter by using the sample information that is taken from that population. For example, we can find the mean of a population by computing the mean of a sample drawn from that population.

#### Estimator

The estimator is a statistic (Rule or formula) whose calculated values are used to estimate (a wise guess from data information) is used to estimate a population parameter $\theta$.

#### Estimate

An estimate is a particular realization of an estimator $\hat{\theta}$. It is the notation of a sample statistic.

#### Types of Estimators

An estimator can be classified either as a point estimate or an interval estimate.

##### Point Estimate

A point estimate is a single number that can be regarded as the most plausible value of the $\theta$ (notation for a population parameter).

##### Interval Estimate

An interval estimate is a set of values indicating confidence that the interval will contain the true value of the population parameter $\theta$.

### Testing of Hypothesis

Testing of Hypothesis is a procedure that enables us to decide, based on information obtained by sampling procedure whether to accept or reject a specific statement or hypothesis regarding the value of a parameter in a Statistical problem.

Note that since we rely on samples, there is always some chance our inferences are not perfect. Statistical inference acknowledges this by incorporating concepts like probability and confidence intervals. These help us quantify the uncertainty in our estimates and test results.

Important Considerations about Testing of Hypothesis

• Hypothesis testing does not prove anything; it provides evidence for or against a claim.
• There is always a chance of making errors (Type I or Type II).
• The results are specific to the chosen sample and significance level.

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