Does hypothesis test ever prove a null hypothesis?

A hypothesis test is fundamentally a "decision-making process that examines a set or sets of data" to determine whether to reject null hypotheses based on expectations under those hypotheses.

Hypothesis testing provides an objective framework for evaluating competing propositions rather than relying on subjective interpretation of raw data. It emphasises that different individuals might form varying conclusions from the same dataset when influenced by chance variation or sampling errors. However, hypothesis tests establish a standardised, consistent decision-making procedure applicable across all users.

Importantly, hypothesis testing is a rejection-focused methodology — it determines whether sufficient evidence exists to reject the null hypothesis, rather than confirming its truth. A failure to reject the null hypothesis does not prove it is true; it simply means there is insufficient evidence against it.