stylistic:style_transfer, linguistic:voice_change
Basic definitions

The null hypothesis and the alternative hypothesis are types of conjectures used in statistical tests to make statistical inferences, which are formal methods of reaching conclusions and separating scientific claims from statistical noise.

The statement being tested in a test of statistical significance is called the null hypothesis. The test of significance is designed to assess the strength of the evidence against the null hypothesis, or a statement of 'no effect' or 'no difference'. It is often symbolized as H.

The statement that is being tested against the null hypothesis is the alternative hypothesis. Symbols may include H and H.

A statistical significance test starts with a random sample from a population. If the sample data are consistent with the null hypothesis, then you do not reject the null hypothesis; if the sample data are inconsistent with the null hypothesis, then you reject the null hypothesis and conclude that the alternative hypothesis is true.

The following adds context and nuance to the basic definitions.

Given the test scores of two random samples, one of men and one of women, does one group score better than the other? A possible null hypothesis is that the mean male score is the same as the mean female score:

where

A stronger null hypothesis is that the two samples have equal variances and shapes of their respective distributions.