# 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 H_{o. }for example if we want to test that the population mean is equal to 400, we can write H_{O}: 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 H_{O}: µ = µ_{O}

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 H_{O}: 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 H_{1.}

If we want to test the null hypothesis

i) H_{O}: µ = 400 it means that the null hypothesis is that the population mean is equal to 400.

ii) H_{O}: 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) H_{O}: 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) H_{O}: 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