## 11.3 Finding the P-Value

The p-value of the ANOVA F-test is the probability of getting an F statistic as large as we got (or even larger) had \(H_0: \mu_1 = \mu_2 = \cdots = \mu_k\) been true. In other words, it tells us how surprising it is to find data like those observed, assuming that there is no difference among the population means \(\mu_1, \mu_2, \ldots, \mu_k\). As we already noticed before, the p-value in our example is so small that it is essentially 0, telling us that it would be next to impossible to get data like those observed had the mean frustration level of the four majors been the same (as the null hypothesis claims).