Why alternative hypothesis could be accepted

Answer 1

The alternative hypothesis can be accepted when there is sufficient evidence to support it. In hypothesis testing, we often set a significance level, which is the probability of incorrectly rejecting the null hypothesis. If the obtained p-value (the probability of obtaining the observed data, or data more extreme, if the null hypothesis is true) is less than the significance level, then we reject the null hypothesis and accept the alternative hypothesis.

Accepting the alternative hypothesis means that there is enough evidence to conclude that the null hypothesis is incorrect, and the alternative hypothesis is more likely to be true. It suggests that there is a significant relationship or difference between the variables being tested.

However, it is important to note that accepting the alternative hypothesis does not guarantee that the alternative hypothesis is absolutely true, but rather that there is strong evidence in favor of it. There is always a possibility of committing a Type I error (false positive) when accepting the alternative hypothesis.