# What is the purpose of hypothesis testing in statistics?

To decide whether the difference between population parameter and the sample statistic is due to chance.

You have population parameter. In some cases, It is a guessed value or assumed value. In some cases, it is already arrived at by some researcher.

Now you want to know it is correct or still persists with the same value.

You conduct a sample study. You get sample statistic.

You compare your value with the population parameter.

There is a fair chance for both to be different.

You want to know whether the difference is real or accidental or by chance (This is sampling fluctuation)

So you go for an appropriate hypothesis test.

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It is a way of finding out if my understanding of the data presented is right.

Statistics is more about study of patterns. The behavior pattern is either explained by, or ascribed to certain well known probability distributions. The probability distributions are

- The Binomial Distribution.
- The Poisson Distribution.
- The Normal Distribution.
- The 't' distribution and so on.
Looking at a sample data, we start with the presumption that this data pattern is that of one of the distributions listed above. The process involved in finding out if our presumption is right or wrong is known as 'testing of hypothesis'. The presumption with which we start is known as a hypothesis. In statistics, the normal practice is to start with a hypothesis that is sought to be rejected more often and hence such a hypothesis is called the null hypothesis.

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The purpose of hypothesis testing in statistics is to make inferences about a population based on sample data. It helps determine whether a claim about the population parameter is supported by the evidence from the sample.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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