If then we fail to reject Null hypotheses (accept it)

In hypothesis testing, when we say that , it means that the p-value calculated from our sample data is greater than the significance level (alpha). This implies that the evidence against the null hypothesis is not strong enough to warrant its rejection, so we “fail to reject” it. However, it’s crucial to understand that failing to reject the null hypothesis doesn’t mean we accept it as true; it simply indicates that we don’t have sufficient evidence to favor the alternative hypothesis.

In practical scenarios, this decision-making process is common in fields like medicine, where researchers often conduct trials to determine the effectiveness of a new drug. If the p-value is high (greater than alpha), it might suggest that the drug does not have a significant effect compared to a placebo. Thus, researchers may decide to keep the current treatment while continuing to explore more data or alternative treatments—emphasizing the iterative nature of scientific inquiry!