## 11.4 Making Conclusions in Context

As usual, we base our conclusion on the p-value. A small p-value tells us that our data contain evidence against \(H_0\). More specifically, a small p-value tells us that the differences between the sample means are statistically significant (unlikely to have happened by chance), and therefore we reject \(H_0\). If the p-value is not small, the data do not provide enough evidence to reject \(H_0\), and so we continue to believe that it may be true. A significance level (cut-off probability) of 0.05 can help determine what is considered a small p-value.

In our example, the p-value is extremely small (close to 0) indicating that our data provide extremely strong evidence to reject \(H_0\). We conclude that the frustration level means of the four majors are not all the same, or, in other words, that majors do have an effect on studentsâ€™ academic frustration levels at the school where the test was conducted.