In statistical analysis, two hypotheses are used. The null hypothesis, or H₀, states that there is no statistical significance between two variables. The null is often the commonly accepted position and is what scientists seek to not support through the study. The alternative hypothesis, or H_a, states that there is a statistical significance between two variables and is what scientists are seeking to support through experimentation.

For example, if someone wants to see how they score on a math test relative to their class average, they can write hypotheses comparing the student’s score, to the class average score (µ). Let’s say for this example, the student’s score on a math exam was 75. The null (H₀) and alternative (H_a) hypotheses could be written as:

In the null hypothesis, there is no difference between the observed mean (µ) and the claimed value (75). However, in the alternative hypothesis, class mean is significantly different (either less than or greater than 75) from the student’s score (75). Statistical tests will be used to support to either support or reject the null hypothesis. When the null hypothesis is supported by the test, then the test indicates that there is not a statistically significant difference between the class mean score and the student’s mean score. If the null hypothesis is rejected, then the alternative hypothesis is supported, which leads to the conclusion that the student’s score is statistically significant difference from the class mean score.