Hypothesis testing is a statistical procedure used to make inferences or draw conclusions about a population based on a sample. It involves formulating a hypothesis, collecting data, and analyzing the data to determine the likelihood of the hypothesis being true.


In hypothesis testing, the null hypothesis (H0) represents the default assumption or the status quo, while the alternative hypothesis (Ha) represents the claim or the new theory being tested. The goal is to either accept or reject the null hypothesis based on the evidence from the data.


The significance level, denoted as α (alpha), is the probability of rejecting the null hypothesis when it is true. It determines the level of confidence required to reject the null hypothesis. Commonly used significance levels are 0.05 (5%) and 0.01 (1%).


A test statistic is a numerical value calculated from the sample data that is used to determine the likelihood of observing the data if the null hypothesis is true. The choice of test statistic depends on the type of hypothesis test being conducted.


The p-value is the probability of obtaining a test statistic as extreme as, or more extreme than, the observed value, assuming that the null hypothesis is true. It provides a measure of the strength of evidence against the null hypothesis. A smaller p-value suggests stronger evidence against the null hypothesis.


The decision rule is a predetermined criterion for accepting or rejecting the null hypothesis based on the p-value. If the p-value is less than the significance level (α), the null hypothesis is rejected. Otherwise, it is not rejected.


Statistical significance refers to the likelihood that the observed results are not due to chance. When a hypothesis test yields a statistically significant result, it suggests that the observed effect is unlikely to have occurred by random variation alone.


In hypothesis testing, a Type I error occurs when the null hypothesis is rejected when it is actually true. On the other hand, a Type II error occurs when the null hypothesis is not rejected when it is false. These errors are inherent in hypothesis testing and should be minimized.


The sample size plays a crucial role in hypothesis testing. A larger sample size increases the power of the test, making it more likely to detect a true effect. Power is the probability of correctly rejecting the null hypothesis when it is false.

In conclusion, hypothesis testing and statistical significance provide a framework for making informed decisions based on sample data. By following these key principles, researchers can assess the strength of evidence against the null hypothesis and draw meaningful conclusions about the population of interest.