The article reviews Karl Pearson's method for testing hypotheses, updates it with modern notation, and extends it to work with various probability distributions. This extension allows for the calculation of exact p-values and acceptance regions for hypotheses under different distributions. It also shows that the method of acceptance intervals by percentiles is a simplified version of Pearson's method. By using the Mahalanobis distance, the method can be applied to distributions of any dimension. This approach provides a historical and comprehensive way to verify or refute hypotheses based on empirical observations.