## 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 students’ academic frustration levels at the school where the test was conducted.