If a hypothesis test yields a p-value of 0.07 and the chosen significance level (alpha) is 0.05, what is the precise and objective conclusion regarding the null hypothesis?

Given a p-value of 0.07 and a chosen significance level (alpha) of 0.05, the precise and objective conclusion is to fail to reject the null hypothesis. The p-value, or probability value, quantifies the strength of evidence against the null hypothesis. Specifically, it is the probability of observing data as extreme as, or more extreme than, the data collected, assuming that the null hypothesis is true. A smaller p-value indicates stronger evidence against the null hypothesis. The significance level, denoted as alpha, is a pre-determined threshold for statistical significance chosen by the researcher before conducting the test. It represents the maximum acceptable probability of making a Type I error, which is the error of incorrectly rejecting a true null hypothesis. The null hypothesis (H0) is a statement of no effect, no difference, or no relationship, which the statistical test aims to find evidence against. The decision rule in hypothesis testing states that if the p-value is less than or equal to alpha (p ≤ α), the null hypothesis is rejected. Conversely, if the p-value is greater than alpha (p > α), we fail to reject the null hypothesis. In this specific scenario, since 0.07 (p-value) is greater than 0.05 (alpha), the observed data does not provide sufficient statistical evidence to reject the null hypothesis at the 0.05 significance level. It is important to understand that failing to reject the null hypothesis does not mean that the null hypothesis is true or proven; it merely means that the available data do not provide compelling enough evidence to conclude that it is false within the specified risk of a Type I error.