Statistical Inference: Overview, Questions, Preparation

Statistics is a mathematical branch that deals with obtaining, analysing, and interpreting any numerical data set presented. It is roughly the analysis of quantitative data. The types of statistics are roughly 2.

• Descriptive Statistics
• Inferential Statistics

What is Inferential Statistics?

Inferential statistics lets you draw an inference from any numerical data set presented. The sample is presented, and data is taken from it. To make an ‘inference’ means to make a rough guess. 

What is the Exact Definition?

Statistical inference is the process of inferring or analysing and arriving at conclusions from the numerical data set presented to you. It is based on random sampling. The purpose is to roughly estimate the uncertainty or variations in the sample. There are 3 components used to make a statistical inference, and they are-

• Sample size.
• Variability in the sample provided.
• Size of the variations observed.

Types of Statistical Inference

There are multiple types of statistical inferences that are used for arriving at the conclusions on a numerical data set.

• One sample hypothesis testing.
• Confidence Interval.
• Pearson Correlation.
• Bi-variate regression.
• Multivariate regression.
• Contingency table.
• ANOVA or T-test.

What is the Procedure for Statistical Inference?

The procedure involved in this is-

1. Understand a theory.
2. Create a hypothesis around that research.
3. Identify the variables.
4. Identify the population on which application must be done.
5. Make a null hypothesis.
6. Accumulate a sample and continue the study.
7. Conduct tests to identify the differences from the null hypothesis.

Statistical Inference Solution 

It deals with all aspects such as collection, analysing, formulating a null hypothesis, and then arriving at a conclusion.

• It is a very common method to understand whether the observed sample is of independent observations from a population type like Poisson or normal.
• It is used to evaluate the parameters of the expected models.

1.Shuffling of a pack of cards is done, the trial is done 400 times, and then a card is drawn from it. They are given as follows.
Spade- 90
Clubs-100
Hearts- 120
Diamonds-90

Solution.

1.If a card is drawn at random. What is the probability of getting a diamond card?
A total number of events is 400.
P of a diamond is 90/400= 0.225
2.If a card is drawn at random. What is the probability of getting a black card?
A total number of events is 400.
P of black card is 190/400=0.475

2.  A bag contains about 2 green balls, 3 blue balls and 5 black balls. One of them is taken out, find the probability that it is black.

Solution.

The total number of bags are 10. 
Probability of getting black balls= 5/10=½=0.5

3. A card is taken out from a pack of 52 cards. What is the probability that it is a face card?

Solution:

Total number of cars= 52
Number of face cards in the pack=13
Therefore the probability is 12/52=3/13

Q: What is Statistical Inference?

Q: What are the three components of statistical inference analysis?

Q: What are the different types of statistical inference?

Q: What are the different applications of statistical inference?

Q: What are the different types of statistics?