Final answer:
The null hypothesis is rejected when the p-value is close to zero, suggesting the observed data are unlikely under the null hypothesis and indicating the alternative might be true.
Step-by-step explanation:
The null hypothesis is most appropriately rejected when the p-value is close to zero. A small p-value indicates that the observed data are very unlikely under the assumption that the null hypothesis is true, which suggests the alternative hypothesis may be the better explanation for the data. Typically, if the p-value is smaller than the significance level, denoted by α; (commonly set at 0.05), we reject the null hypothesis in favor of the alternative.
For example, if you are conducting a two-tailed hypothesis test with a significance level of 0.01, any p-value less than 0.01 would lead to rejection of the null hypothesis. Therefore, p-values that are less than the established α value provide support to the alternative hypothesis and are a basis to reject the null hypothesis.