The question is about hypothesis testing and its use in analysis for various disciplines, including mathematics, psychology, medicine, and engineering.
Hypothesis testing gives a framework to evaluate the relationship between variables.
To formulate hypotheses, you should determine the null hypothesis H0, which assumes no relationship between the variables and alternative hypothesis H1, which assumes there is a relationship or effect. After that you will apply the suitable statistical tests for your variables and interpret the result, if significance results obtained so the alternative hypothesis is approved.
Hypothesis is a statement about the population parameter (unknown quantity) for this purpose we conduct the survey or collect the data for the relevant facts and after gathering the data we apply useful test .
Like for comparison of means we use t test when variation of the population not known, ANOVA to compare multiple group means.
Correlation to find the relationship between variables, linear regression to set a formula by which these variables are related.
Simply put, let's say your study has a set of variables with relationships based on some form of theoretical background or conceptualization.
As a researcher, you attempt to prove that these relationships exist or otherwise in a population.
As a result, you develop a set of statements (hypotheses) based on the relationships which you subsequently subject to statistical testing (hypotheses testing) to 'verify' if they truly exist or not in that population.
The use of a hypothesis can be used to determine the statistical analysis you wish to use for your study/research. The null hypothesis is the baseline (typically zero, but could be a number. e.g. population mean) and that is used to compare DIFFERENCES between the null (0) and your data. Relationships on the other hand are usually measured using correlations. Correlations (Pearson's R) are measured on STRENGTH of the relationships (strong, moderate, weak, etc.) In any case - if you are looking for statistical significance, your results need to be + or - 2 standard deviations (roughly). If that occurs you can reject the null (H0) and say your results are statically significant (something special occurred in your data - most often supporting further research/analysis).
Hypotheses point the way to choosing variables to interrelate, designing studies to do so, and statistically analyzing the resultant data. The alternative is "investigative questions" which strike me as "pre-hypotheses". That is, one knows what variables to interrelate, but has no preconception as to the results.
Investigations based on hypotheses could conceivably see statistical analysis by one-tailed tests, but, in practice, rarely do. Those based on investigative questions require and typically receive two-tailed tests. An occasionally employed but questionable tactic is "HARKING", i.e., hypothesizing after the results are known. This can take place when the study followed an investigative question or an incorrect hypothesis (replaced in reporting by the "correct" hypothesis).