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# Statistical Inference

Statistical inference solution creates an efficient use of numerical data connecting to groups of individuals or experiments. It deals with all aspects including the collection, study and explanation like data and planning the collection of data. By statistical inference solution, people can get knowledge after beginning their work in several fields. There is also a regulation known as mathematical statistics, which is related with the theoretical root of this topic.

 Related Calculators Calculate Statistics Calculating T Test Statistic Chi Square Statistic Calculator F Test Statistic

## Statistical Inference Definition

Statistical inference is the process of drawing conclusions from data subject to random variation also called inferential statistics. Test of hypotheses and confidence intervals are the applications of the statistical inference. Statistical inference is a method and practice of forming judgments about the parameters of a population on the basis of random sampling.

## Probability and Statistical Inference

The collection of the observation that are obtained from any trial is often called a sample. The making of a conjecture about a distribution of a random variable based on the sample is called a statistical inference. To understand the concept behind statistical inference made from the sample, we need a knowledge of some probability, basic distributions and sampling distribution theory.

## Statistical Inference Solution

Below are the facts meant by statistical inference solution:

• Goal for residue of region is to know about probability to help us analyze data .
• This is a common approach to assume that observed sample are independently observations from a population model like Poisson or normal.
• Statistical inference solution is used to to estimate the parameter(s) of the assumed model like normal mean or binomial proportion.

## Statistical Inference Examples

Given below are some of the examples on Statistical Inference.

### Solved Examples

Question 1: A card is drawn from a shuffled pack of cards. This trial is repeated 400 times and suits are given below.

 Suit Spade clubs Hearts Diamond No. of times drawn 90 100 120 90

While a card is tired at random what is the probability that it is

a) To got a diamond cards

b)To got a black cards

Solution:

By statistical inference solution

Given:
Total number of events = 90 + 100 + 120 + 90 = 400

a) To got a diamond cards
Number of trials in which a diamond drawn = 90

P (the card drawn is a diamond) = $\frac{90}{400}$ = 0.22

b) To got a black cards

Number of times a black card showed up = 90 + 100 = 190

P (the card drawn is black) =  $\frac{190}{400}$ = 0.48

Number of times a card other than a spade showed up = 100 + 120 + 90 = 310

P (the card is not a spade)$\frac{310}{400}$ = 0 .78

Question 2: When one review conducted among 500 students each one can speak either Hindi or English or both, it was found that 300 of them could speak Hindi and 350 of them could speak English. While a student can selected at random, what is the probability that he can speak two languages?
Solution:

Let probability of the student who speaks two languages = A

By statistical inference solution,

Here is a step by step explanation by statistical inference solution,

Step 1:

Total number of students = 500

Number of student speaks Hindi, P(H) = 300

Number of student
speaks english, P(E) = 350

Step 2:
We know,

P(H $\cup$ E) = P(H) + P(E) - P(H $\cap$ E)

=> 500 = 300 + 350 - P(H $\cap$ E)

=> P(H $\cap$ E) = 650 - 500

= 150

=> Number of students who can speak both languages = 150

Step 3:

Now, a student can selected at random who can speak two languages.

=> P(A) = $\frac{150}{500}$ = 0.3

 More topics in Statistical Inference Non Parametric Test Likelihood Ratio Test Point Estimate
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