Final answer:
If the null hypothesis is rejected in favor of the alternative hypothesis, it implies there is sufficient evidence to support the alternative hypothesis. Rejection is based on sample data and probability calculations. It indicates the data are inconsistent with the null hypothesis and suggests the alternative hypothesis is more likely.
Step-by-step explanation:
In hypothesis testing, if the null hypothesis has been rejected when the alternative hypothesis is true, it can be concluded that there is enough evidence to support the alternative hypothesis. It's important to remember that hypothesis testing is based on the probability of observing the data if the null hypothesis were true, not on absolute certainties. Rejecting the null hypothesis does not prove the alternative hypothesis; it simply indicates that the data are unlikely under the null hypothesis and are more consistent with the alternative hypothesis.
Note that when we reject the null hypothesis, we are making a decision based on the evidence at hand. We never state that a claim is proven true or false absolutely; rather, we indicate that the evidence suggests the alternative hypothesis is more likely to be true than the null hypothesis. This decision is based on the level of significance and the p-value obtained in the hypothesis testing.
A rejection of the null hypothesis implies that the test was conducted correctly under the assumption that the analysis was performed using the correct distribution and that the conditions for the test were met. However, rejecting the null does not completely rule out the possibility of a Type I error, where the null hypothesis is mistakenly rejected even though it is true.