In hypothesis testing, the null hypothesis (H0) and the alternative hypothesis (Ha) are two competing statements about a population parameter or the relationship between variables. These hypotheses are formulated based on the research question or the objective of the study.

The null hypothesis (H0) represents the default or the no-change position. It states that there is no significant difference, relationship, or effect in the population. In other words, any observed difference or relationship in the sample is due to random chance. The null hypothesis is typically denoted as H0: parameter = value or H0: population characteristic = value.

The alternative hypothesis (Ha) is the statement that contradicts the null hypothesis. It represents the researcher’s claim, belief, or expectation about the population parameter or the relationship between variables. It states that there is a significant difference, relationship, or effect in the population. The alternative hypothesis can be one-sided (one direction) or two-sided (two directions). The alternative hypothesis is typically denoted as Ha: parameter ≠ value or Ha: population characteristic ≠ value (for a two-sided test).

The choice between the null and alternative hypotheses depends on the research question and the desired outcome of the study. The researcher formulates the hypotheses based on prior knowledge, existing theories, or expected outcomes.

During hypothesis testing, the researcher collects data and performs statistical analysis to evaluate the evidence against the null hypothesis. The analysis involves calculating a test statistic and comparing it to a critical value or calculating a p-value. The decision is then made whether to reject the null hypothesis in favor of the alternative hypothesis or fail to reject the null hypothesis.

If the evidence is strong enough, and the test statistic falls in the critical region (the rejection region), the null hypothesis is rejected, and the alternative hypothesis is supported. This implies that there is evidence to suggest that the population parameter is different from the hypothesized value, or there is a relationship between variables.

If the evidence is not strong enough, and the test statistic falls outside the critical region, the null hypothesis is not rejected. This does not provide sufficient evidence to conclude that there is a significant difference or relationship in the population.

It’s important to note that failing to reject the null hypothesis does not prove that the null hypothesis is true, but rather indicates that there is not enough evidence to support the alternative hypothesis.

In summary, the null hypothesis represents the default position of no significant difference or effect, while the alternative hypothesis represents the researcher’s claim or expectation. Hypothesis testing involves analyzing data to make a decision about accepting or rejecting the null hypothesis based on the evidence obtained from the sample.