# Null hypothesis and Alternative hypothesis

Let us discuss the difference between null and alternative hypothesis:

Null hypothesis

The hypothesis we want to test or a hypothesis of no difference is called null hypothesis. It is denoted by Ho. for example if we want to test that the population mean is equal to 400, we can write HO: µ : 400 and we read it as “ the null hypothesis is that the population mean is equal to 400.

1)      Null hypothesis is expressed in equality like HO: µ = µO

2)      We set up null hypothesis to test the significance of difference between a statistic and parameter. For example if we want to test that a particular medicine is effective or not than we shall set up a null hypothesis that is not effective.

3)      If we want to test any statement we set up null hypothesis that it is true. For example population mean has a specified value 400. Then the null hypothesis will be HO: µ = 400.

Alternative hypothesis

The hypothesis which is complementary to null hypothesis is alternative hypothesis. When we accept the null hypothesis, it means we reject the alternative hypothesis. It is denoted by H1.

If we want to test the null hypothesis

i)                    HO: µ = 400 it means that the null hypothesis is that the population mean is equal to 400.

ii)                  HO: µ ≠ 400 it means that the alternative hypothesis is that the populations mean is not equal to 400. It is a two tailed alternative hypothesis.

iii)                HO: µ >400 it means that the null hypothesis is that the population mean is greater than 400. It is a right tailed alternative hypothesis.

iv)                HO: µ <400 it means that the null hypothesis is that the population mean is less than 400. It is a left tailed alternative hypothesis.

This is the difference between null and alternative hypothesis