# Statistical Inference

In Statistics, descriptive statistics describe the data, whereas inferential statistics help you make predictions from the data. In inferential statistics, the data are taken from the sample and allows you to generalize the population.

## Statistical Inference Definition

Statistical inference is the process of analysing the result and making conclusions from data subject to random variation. It is also called inferential statistics. Hypothesis testing and confidence intervals are the applications of the statistical inference. Statistical inference is a method of making decisions about the parameters of a population, based on random sampling. It helps to assess the relationship between the dependent and independent variables. The ingredients used for making statistical inference are:

- Sample Size
- Variability in the sample
- Size of the observed differences.

## Types of Statistical Inference

There are different types of statistical inferences that are extensively used for making conclusions. They are:

- One sample hypothesis testing
- Confidence Interval
- Pearson Correlation
- Bi-variate regression
- Multi-variate regression
- Chi-square statistics and contingency table
- ANOVA or T-test

## Statistical Inference Procedure

The procedure involved in inferential statistics are:

- Begin with a theory
- Create a research hypothesis
- Operationalize the variables
- Recognize the population to which the study results should apply
- Formulate a null hypothesis for this population
- Accumulate a sample of children from the population and continue the study
- Conduct statistical tests to see if the collected sample properties are adequately different from what would be expected under the null hypothesis to be able to reject the null hypothesis

## Statistical Inference Solution

Statistical inference solutions produce efficient use of statistical data relating to groups of individuals or trials. It deals with all characters, including the collection, investigation and analysis like data and organizing the collection of data. By statistical inference solution, people can acquire knowledge after starting their work in diverse fields. Some statistical inference solution facts are:

- It is a common way to assume that the observed sample is independent observations from a population type like Poisson or normal
- Statistical inference solution is used to evaluate the parameter(s) of the expected model like normal mean or binomial proportion

### Statistical Inference Examples

An example of statistical inference is given below.

**Question: **From the shuffled pack of cards, a card is drawn. This trial is repeated for 400 times, and the suits are given below:

Suit |
Spade |
Clubs |
Hearts |
Diamonds |

No.of times drawn |
90 |
100 |
120 |
90 |

While a card is tried at random, then what is the probability of getting a

- Diamond cards
- Black cards
- Except for spade

**Solution:**

By statistical inference solution,

Total number of events = 400

i.e.,90+100+120+90=400

**(1) The probability of getting diamond cards:**

Number of trials in which diamond card is drawn = 90

Therefore, P(diamond card) = 90/400 = 0.22

**(2) The probability of getting** **black cards:**

Number of trials in which black card showed up = 90+100 =190

Therefore, P(black card) = 190/400 = 0.48

**(3) Except for spade **

Number of trials other than spade showed up = 90+100+120 =310

Therefore, P(except spade) = 310/400 = 0.78