Final answer:
In statistics, the null hypothesis (H₀) asserts no difference or effect and is assumed to be true, while the alternative hypothesis (Hₐₓ) posits some effect or difference. Evidence from the sample data is used to decide whether to reject H₀. The process follows probability laws, meaning conclusions aren’t stated as absolute truths.
Step-by-step explanation:
In statistics, when conducting a hypothesis test, we begin by formulating two types of hypotheses: the null hypothesis (symbolically represented as H0) and the alternative hypothesis (symbolically represented as Ha).
The null hypothesis typically states that there is no effect or no difference, and it is assumed true until evidence suggests otherwise. It often specifies that the population parameter (such as µ or p) is equal to a certain value. In contrast, the alternative hypothesis posits that there is an effect or a difference. It may suggest that a population parameter is not equal to a certain value, is greater than, or is less than a certain value, depending on the direction of the test.
When evaluating sample data, we look for evidence that would lead us to reject the null hypothesis in favor of the alternative hypothesis. However, we never state that the null hypothesis is proven true or false, as hypothesis testing is governed by the laws of probability, which do not deal in absolutes.
An example of a null hypothesis could be "All groups have the same mean (µ = µ0)", whereas an alternative hypothesis could say "At least one group has a different mean (µ ≠ µ0)" for tests that compare group means.