** Research Hypothesis:** The second important step in the formulation of a research problem is the construction of a hypothesis. The hypothesis is a tentative solution to a problem. It is a specific, testable prediction about the research study. A scientist needs to understand the meaning and nature of a hypothesis. The hypothesis needs to be clear, precise, and capable of being tested.

The hypothesis is a tentative statement about the solution to the problem. The term hypothesis has been defined in several ways. A hypothesis is a provisional formulation or possible solution or tentative explanation or suggested answer to the problem being faced by the researcher.

A hypothesis is an important part of scientific research. The importance of hypothesis is generally recognized more in the studies which aim to make predictions about some outcome. In experimental research, the scientists are interested in making predictions about the outcome of the experiment and hence, the role of hypothesis is most important. In historical or descriptive research, the researcher is investigating the history of a nation or a village and thus may not have a basis for predicting results. Therefore, a hypothesis may not be required in such fact-finding studies. If a researcher is tracing the history of a university or making a study about the results of a coming Loksabha election, the facts or data he gathers will prove useful only if he can draw generalizations from them. A hypothesis is recommended for all major studies to explain observed facts, conditions, or behavior and to serve as a guide in the research studies. A working hypothesis or a tentative hypothesis is described as the best guess or statement derivable from the known or available evidence. The amount of evidence and quality, of it, determine other forms of hypothesis.

**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. |

**Hypothesis Testing**

Hypothesis testing is a process of deciding statistically whether the findings of a research show chance or real effects at a given level of probability. Hypothesis testing is depending on probability theory and sampling. It consists of stating the hypothesis (null or alternative) construction of data gathering tools, collection of data, statistical analysis, and drawing inferences from the results, Research in which the independent variable is manipulated is called ‘experimental hypothesis-testing research’ and research in which an independent variable is not manipulated is called ‘non-experimental hypothesis-testing research. Some of the important concepts in the context of testing of hypothesis are as follows:

**Null Hypothesis and Alternative Hypothesis:**

If two methods are compared about their superiority and proceed on the assumption that both methods are equally good, then this assumption is called a null hypothesis (H_{o}). It may conclude that method A is superior to method B then it is called the alternative hypothesis (H_{o}). Both hypotheses are chosen before the sample is drawn. Generally, in hypothesis testing, the researcher can proceed based on the null hypothesis, keeping the alternative hypothesis in view. A researcher can assign the probabilities to different possible sample results if the null hypothesis is true, but this cannot be done if proceed with the alternative hypothesis. Hence, the use of the null hypothesis is quite frequent.

**The Level of Significance:**

This is the essential concept of hypothesis testing and is always considered in percentages (normally 5%). The significance level is the maximum value of the probability of rejecting a null hypothesis when it is true. It is usually determined in advance before testing the hypothesis. For example, if you assume the significance level to be 5%, it means that the researcher is ready to take a 5% risk to reject the null hypothesis when it happens to be true.

**P-Value:**

The p-value is the level of marginal significance within a statistical hypothesis test representing the probability of the occurrence of a given event. The p-value is used as an alternative to rejection points to provide the smallest level of significance at which the null hypothesis would be rejected. A p-value is used in hypothesis testing to help you support or reject the null hypothesis.

**Decision Rule or Test of Hypothesis:**

A researcher can design a rule which is known as a decision rule according to which it may accept H_{o}. (reject H_{a}) or reject H_{o}, (accept H_{a}). The researcher must decide the number of items to be tested and the criterion for accepting or rejecting the hypothesis. For example, if five items are tested in the lot and plan the decision that null hypothesis will be accepted only if out of those five items, either none is defective or only 1 is defective; otherwise alternative hypothesis will be accepted.

**Two-tailed and One-tailed Test:**

In the context of hypothesis testing, two-tailed tests and one-tailed tests are important and must be clearly understood by the researcher. A two-tailed test rejects the null hypothesis if the sample mean is either more or less than the hypothesized value of the mean of the population. The test is appropriate when the null hypothesis is some specific value and the alternative hypothesis is a value not equal to the specified value of the null hypothesis. In a two-tailed curve, there are two rejection regions also called critical regions. When the population means is either lower or higher than some hypothesized value, the one-tailed test is considered to be appropriate. If the rejection area is only on the left tail of the curve, then this is known as the left-tailed test.

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