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## Inferential Statistics

Last Updated: Jan 10, 2022
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# Hypothesis Testing

Hypothesis testing or significance testing is a method for testing a claim or hypothesis about a parameter in a population, using data measured in a sample. In this method, we test some hypotheses by determining the likelihood that a sample statistic could have been selected, if the hypothesis regarding the population parameter were true.

The method of hypothesis testing can be summarized in four steps:

1. State the hypothesis. This means identifying the hypothesis or claim to be tested or validated.
2. Set the criteria for decision. Selecting the criterion upon which it will be tested or deciding that the claim is true or not.
3. Compute the test statistics. Take a random sample from the population and measure the test statistics for example mean of the sample.
4. Compare the observations and decide whether the hypothesis is true or not.

Putting in simpler terms, the goal of hypothesis testing is to determine the likelihood that a population parameter is likely to be true. We simply start by stating a claim on a population parameter, say mean of the population to carry some value and we conduct a series of tests to validate that the claim is true, or not. What is stated as a claim in the first step is called a Null Hypothesis. And the tests are carried out to decide whether the Null hypothesis is true or it needs to be rejected.

Now, why do we need to test the Null hypothesis in the first place? Because it’s an assumption or claim we make, and we think it’s wrong. To counter, we state an alternative hypothesis that says what’s wrong with the Null hypothesis. An alternative hypothesis is a statement that directly contradicts a null hypothesis by stating that the actual value of a population parameter is less than, greater than, or not equal to the value stated in the null hypothesis.

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Hypothesis Testing
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Central Limit Theorem
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Distribution Analysis: Multivariate
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Estimation and Sampling

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