What is a hypothesis that states that there is no relationship between two phenomena under consideration?

In inferential statistics, the null hypothesis (often denoted H0) is a default hypothesis that a quantity to be measured is zero (null). Typically, the quantity to be measured is the difference between two situations, for instance to try to determine if there is a positive proof that an effect has occurred or that samples derive from different batches.

The null hypothesis is effectively stating that a quantity (of interest) is larger or equal to zero and smaller or equal to zero. If either requirement can be positively overturned, the null hypothesis is "excluded from the realm of possibilities".

The null hypothesis is generally assumed to remain possibly true. Multiple analyses can be performed to show how the hypothesis should either be rejected or excluded e.g. having a high confidence level, thus demonstrating a statistically significant difference. This is demonstrated by showing that zero is outside of the specified confidence interval of the measurement on either side, typically within the real numbers. Failure to exclude the null hypothesis (with any confidence) does not logically confirm or support the (unprovable) null hypothesis.