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 disprove. The alternative hypothesis, or Ha, states that there is a statistical significance between two variables and is what scientists are seeking to prove through experimentation. For example, if someone wants to see how they score on a math test relative to their class average, they can draw hypotheses comparing the observed mean, or the student’s score (µ), to the claimed value, or class average score. Let’s say for this example, the class average on a math exam was 75:
H0: There will be no significant statistical difference between the student’s score and the class average score on the math exam.
H0: µ = 75
H0: µ = µ0
Ha: There will be a statistically significant difference between the student’s score and the class average score on the math exam.
Ha: µ ≠ 75
Ha: µ ≠ µ0
In the null hypothesis, there is no difference between the observed mean (75) and the claimed value (75). However, in the alternative hypothesis the observed mean (less than or greater than 75) is significantly different than the claimed value (75).