Question

What is the purpose of hypothesis testing in statistics?

Answer 1

Here we will understand the meaning of a statistical hypothesis and then we will see the definition of hypothesis testing. Further we will understand about the null hypothesis and the alternative hypothesis and their uses. In the end we will take an example of flipping a coin and see the case in which we reject the null hypothesis and the case in which we accept it.

Complete step by step solution:
Now, in mathematics a statistical hypothesis is a hypothesis that is testable on the basis of observed data modelled as the realised values taken by a collection of random variables. A statistical hypothesis test is a method of statistical inference, which is the process of using data analysis to infer properties of an underlying distribution of probability.
We use the hypothesis test to determine if we have to reject the null hypothesis or the alternate hypothesis. A null hypothesis, denoted with ${{H}_{0}}$, is a hypothesis associated with a contradiction to a theory one would like to prove. An alternative hypothesis, denoted with ${{H}_{1}}$, is a hypothesis associated with the theory one would like to prove.
Let us consider an example of flipping a coin and check the case where we reject the null hypothesis or the alternative hypothesis. A person wants to test that a coin has exactly a 50% chance of landing on heads, the null hypothesis would be that 50% is correct and the alternative hypothesis would be that 50% is not correct. Therefore, mathematically we have ${{H}_{0}}=0.5$ and ${{H}_{1}}=0.5$.
We consider a random sample of 100 coin flips is taken and in we take two cases: - in the first case we get 70 tails and 30 heads then in such a case we have to consider that the coin does not have a 50% chance of landing on heads and we will reject the null hypothesis and accept the alternative hypothesis. In the second case we get 49 heads and 51 tails then in such a case we accept the null hypothesis.

Note: You must remember the definitions of certain terms of statistics used in higher mathematics to solve the above question. There are two types of errors where in Type 1 error we wrongly reject the null hypothesis and in Type 2 error the null hypothesis is wrongly not rejected. There are many famous examples of hypothesis testing like: - Lady tasting tea, Courtroom trial, Philosopher’s beans etc. which can be read.