Ho, and Ha, because English is ho: null hypothesis, are used to represent the default hypothesis, that is, the situation opposite to the hypothesis, and ha: alternative hypothesis is used to represent the hypothetical and expected situation. Write Ha omitting Ho, so you have h 1, h2, h2 (it is H 1a, H2a, H3a, which is not written as H 1o, H2o, H3o by default).

Historical background:

Statistics originated from the study of social and economic problems. In the development process of more than 2,000 years, statistics has experienced at least three stages of development: city-state politics, political arithmetic and statistical analysis science.

The so-called "mathematical statistics" is not a new discipline independent of statistics. To be exact, it is the general name of all the new methods of collecting and analyzing data formed in the third development stage of statistics. Probability theory is the theoretical basis of mathematical statistics, but it belongs to mathematics rather than statistics.