[Maths Class Notes] on Statistical Inference Pdf for Exam

What are the two Types of Statistical Inference?

Although, there are different types of statistical inference that are used to draw conclusions such as Pearson Correlation, Bi-varaite Regression, Multivariate regression, Anova or T-test and Chi-square statistic and contingency table.

But, the most important two types of statistical inference that are primarily used  are

• Confidence Interval

• Hypothesis testing

Statistical Inference Procedure

Following Steps are Included in the Statistical Inference Procedure

1. Start with a theory

2. Design  research hypothesis

3. Implement the variables

4. Acknowledge the population to which the results should be applied.

5. Draw up the null hypothesis for this population.

6. Assemble the sample of children from the population and begin the study.

7. Implement the statistical test to examine if the collected sample properties are sufficiently different from what is expected under the null hypotheses to be able to reject the null hypothesis.

Statical Interference Solutions

Statistical inference solutions deliver efficient use of statistical data with respect to the group of individuals or trials. It manages with every character,including the collection, investigation and analysis of data and organizing the collection of data. Through statistical inference solutions, people can gain knowledge after initiating their work in multiple fields. Some of the statistical inference solution facts are as follows:

• It is a usual method to predict that the observed samples are independent observations from a population type such as poison or normal.

• Statistical inference solution helps to evaluate the parameter(s) of the expected model such as normal mean or binomial proportion.

Importance of Statistical Inference

Statistical Inference is significant to examine the data properly. To make an effective solution, accurate data analysis is important to interpret the results of the research. Inferential statistics is used in the future prediction for varied observations in different fields. It enables us to make inferences about the data. It also helps us to deliver a probable range of values for the true value of something in the population. Statical inference is used in different fields such as:

• Business Analysis

• Artificial Intelligence

• Financial Analysis

• Fraud Detection

• Machine Learning

• Pharmaceutical Sector

• Share market.

What is Statistical Inference Example

The Statistical Inference example is given below help you to understand the concepts clearly:

From the Shuffled Pack of 52 Cards, a Card is Drawn. The Trial is Repeated for a Maximum of 400 Times and Different Suits of Cards are Given Below :

What is the probability of getting the following suits, if the card is drawn randomly 

1. Diamond Card

2. Black Card

3. Except for spade

Solution: Through statistical inference solution. 

Total number of events = 400

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

1. The probability of winning a diamond card is :

Total number of trials in which diamond card is drawn= 90

Hence, P(diamond card )= 90/4000

= 0.22

2. The probability of winning black card is :

Number of trial in which black card appeared = 100 + 90 = 190

Hence, P(black card) = 190./400 = 0.48

3. Except spade

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

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

Solved Examples

1. A bad containing 2 yellow balls, 3 red balls, and 5 black balls. Only one ball is drawn at random from the bag. What is the probability that the black ball is drawn?

Solution: Through statistical inference solution.

Total number of balls in a bag = 10

i.e 2 + 3+ 5 = 10

Number of black balls= 5

Probability of getting a black balls =  Number of balck balls/ Total number of balls

 = 5/10 

= 1/2

Hence, the probability of getting black balls is 1/2.

2. A card is drawn from a pack of 52 cards. What is the probability that the card drawn is a face card ( Jack, King and Queen only)?

Solution: Total number of cards= 52

Number of a  face card in a pack of 52 cards= 12

Probability of receiving  a  face card = 12/52 = 3/13

Hence, the probability of receiving face card is 3/13

Facts 

• The birth date of statistics is 1662 when John Gaunt and William Petty originated early human statical and census methods that deliver a framework for modern demography.

• Sir Ronald Fisher, a British Mathematician and Biologist is the father of modern statistics and experimental design.

• Statistics was called the science of state or the science of kings in ancient times. As it was used by States or KIngs.

Quiz Time

1. Which of the given below is considered as a random variable?

1. The outcome from a roll of the die

2. The outcome of the flip of a coin

3. The outcome of the exam

4. All of the above

2. Statistical inference is the method of drawing the formal concl
usion form the given data

1. True 

2. False

3. Hypothesis testing and estimation are the two important branches of the field of inferential statistics.

1. True

2. False

4. The optimum use of the laws of probability to make an inference and draw the statical conclusion about the population on the basis of sample data is referred to as 

1. Descriptive statistics

2. Inferential statistics

3. Sample Statistics

4. Population Statistics