**Null Hypothesis**

A null hypothesis is a hypothesis that shows there is no statistical significance between the two variables in the hypothesis. The null hypothesis is a non-directional hypothesis that proposes no relationship between two variables. For example, there is no significant difference in academic performance of college students who participate in sports and sports non-participating students. Since a null hypothesis can be statistically tested then it is called. ‘statistical hypothesis’. They are also called the testing hypothesis by converting them into null form. The proponents of the null hypothesis emphasize that the researcher must remain unbiased throughout the study. The researcher may reject the null hypothesis by showing that the outcome mentioned in the declarative hypothesis does occur. The quantum of it is such that it cannot be easily dismissed as having occurred by chance. It is the hypothesis that the researcher tries to disprove.

If the hypothesis is that “the consumption of a particular medicine reduces the chances of heart arrest”, the null hypothesis will be “the consumption of the medicine doesn’t reduce the chances of heart arrest. “If the hypothesis is that, “If random test scores are collected from men and women, does the score of one group differ from the other?” a possible null hypothesis will be that the mean test score of men is the same as that of the women.

**Ho: µ₁ = µ₂**

Where

- H
_{o}= Null hypothesis, - µ₁ = Mean of population 1, and
- µ₂ = Mean of population 2.

A stronger null hypothesis is that the two samples are drawn from the same population, such that the variances and shapes of the distributions are also equal.

Statistical hypotheses are tested using a four-step process. The first step is for the analyst to state the two hypotheses so that only one can be right. The next step is to formulate an analysis plan, which outlines how the data will be evaluated. The third step is to carry out the plan and physically analyze the sample data. The fourth step is to analyze the results and either reject the null hypothesis or claim that the observed differences are explainable by chance alone.

The principle of the null hypothesis is collecting the data and determining the chances of the collected data in the study of a random sample, proving that the null hypothesis is true. In situations or studies where the collected data doesn’t complete the expectation of the null hypothesis, it is concluded that the data doesn’t provide sufficient or reliable pieces of evidence to support the null hypothesis and thus, it is rejected.

**Alternative Hypothesis**

Alternative hypothesis defines is a statistically important relationship between two variables. The alternative or experimental hypothesis reflects that there will be an observed effect for our experiment. It is contradictory to the null hypothesis (Table) and denoted by H_{a }or H₁. In many cases, the alternate hypothesis will just be the opposite of the null hypothesis. For example, the null hypothesis might be There was no change in the water level this spring, and the alternative hypothesis would be There was a change in the water level this spring”. The alternative hypothesis is the hypothesis that is to be proved that indicates that the results of a study are significant and that the sample observation is not results just from chance but from some non-random cause. It is a hypothesis that the researcher tries to prove.

Basically, there are three types of alternative hypotheses.

**(a) Left-Tailed:** Here, it is expected that the sample proportion (µ₁) is less than a specified value which is denoted by µ₂ such that:

**H _{1}: µ₁ ˂ µ₂**

**(b) Right-Tailed:** It represents that the sample proportion (π) is greater than some value, denoted by π_{o}.

**H _{1}: µ₁ > µ₂**

**(c) Two-Tailed:** According to this hypothesis, the sample proportion (denoted by π) is not equal to a specific value which is represented by π_{o}.

**H _{1}: µ₁ **

**≠**

**µ₂**

**The null hypothesis for all the three alternative hypotheses would be H₁:** **µ₁ = µ₂**. If the null hypothesis is rejected, then we accept the alternative hypothesis. If the null hypothesis is not rejected, then we do not accept the alternative hypothesis.

An alternative hypothesis provides the researchers with some specific restatements and clarifications of the research problem. The alternative hypothesis is important as they prove that a relationship exists between two variables selected and that the results of the study conducted are relevant and significant.

**Difference Between Null Hypothesis and Alternative Hypothesis**

Null Hypothesis | Alternative Hypothesis |

1. This hypothesis states that there is no relationship between the two phenomena under consideration or that there is no association between the two groups. | 1. Alternative hypothesis states that there is a relationship between two selected variables in a study. |

2. It is denoted by H_{o}. | 2. It is denoted by H₁ or H_{a}. |

3. It is followed by the ‘equals to’ sign. | 3. It is followed by not equals to, ‘less than’ or ‘greater than’ sign. |

4. The researcher tries to prove the alternative hypothesis. | 4. The researcher tries to disprove the null hypothesis. |

5. This hypothesis believes that the results are observed as a result of chance. | 5. The alternative hypothesis believes that the results are observed as a result of some real causes. |

6. The result of the null hypothesis indicates no changes in opinions or actions. | 6. The result of an alternative hypothesis causes a change in opinions and actions. |

7. If the null hypothesis is accepted, the results of the study become insignificant. | 7. If the alternative hypothesis is accepted, the results of the study become significant. |

8. If the p-value is greater than the level of significance, the null hypothesis is accepted. | 8. If the p-value is smaller than the level of significance, a hypothesis is accepted. |

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