Hypothesis Testing Basics

A
hypothesis is a statement that sets forth what we believe to be true
about the relationships among the characteristics being studied. The
null hypothesis, denoted by H_{o}, initially assumed to be
true, assumes that differences do not exist or relationships among the
characteristics are due to chance. The alternative hypothesis, denoted
by H_{A}, assumes
that there are real differences between the characteristics being
studied, or there are factors that have a real influence on the study
outcomes.

Hypothesis Test Example

A college would like to determine if the average GPA of their male and female freshmen students is the same.

Η_{0} : *μ*_{male} = *μ*_{female}Η_{A} : *μ*_{male} ≠ *μ*_{female}

The null hypothesis is that the GPA mean for male freshmen is equal to the female GPA mean (where *μ* represents the mean). The alternative hypothesis is that the average freshmen male and female GPAs are different.