In Maths, Statistics is a concept which deals with research and analysis of numerical data. It sometimes happens that we are not provided with accurate data sets; then we consider the hypothesis. Basically, there are two types of Hypothesis: Null Hypothesis and Alternative Hypothesis.

A **hypothesis** is a consideration or theory based on inadequate evidence that confers itself to advance testing and experimentation. With additional testing, a prediction can generally be demonstrated as true or false.

The null hypothesis is sometimes rejected too. If this assumption is rejected, it means that analysis could be unreasonable. Many researchers will ignore this hypothesis as it is slightly opposite the alternative hypothesis. It is a better method to create a theory and test it. The aim of researchers is not to discard the hypothesis. But it is proof that a certain statistical model is always connected with the failure to decline the null hypothesis.

## Null Hypothesis in Statistics

A null hypothesis is a theory that assumes there is no statistical importance between the two variables in the hypothesis. It is the assumption that the researcher is seeking to expose. For example, there is no statistically meaningful relationship between the type of water fed to the plants and growth of the plants. A researcher is questioned by the null hypothesis and normally wants to deny it, to illustrate that there is a statistically vital relationship between the two variables in the hypothesis.

Learn in detail about Null Hypothesis here.

## Symbol

In statistics, the symbol of the null hypothesis is denoted by, H_{0}, i.e., letter H with subscript ‘0’ (zero). It is referred to as H-null or H-zero or H-nought. Whereas, the alternative hypothesis represents the observations defined by the non-random condition. It is represented by H_{1} or H_{a}.

**Also, read:**

## Formula

**Null hypothesis formula:**

H_{0}: p = p_{0}

p=mean of population 1

p_{0}=mean of population 2

Alternative hypothesis formula is:

H_{a} : p ≠ p_{0} (p >p_{0})

Test static formula is:

\(z=\frac{P-p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}}\)## Null and Alternative hypothesis

**Alternative hypothesis** defines there is a statistically meaningful relationship between two quantities or variables. Whereas **null hypothesis** states, there is no statistical correlation between the two variables.

The conclusions of null hypothesis are the outcome of possibility and the result of the alternative hypothesis is the outcome of real effect.

The mathematical formulation is an equal sign for null hypothesis, whereas for the alternative hypothesis, it is an inequality sign like greater than (>), less than (<), etc

## Examples of Null Hypothesis

- There could be the possibility of getting deceased by typhoid but not 100%.
- There is no age limit to using mobile phones to access the internet.
- Having an apple a day does not ensure that we would not get a fever, but it helps to boost immunity to fight against the disease.