Hello,

The Null Hypothesis (H_0) is a statement or assumption in statistical testing that proposes no significant difference, effect, or relationship exists in a population or dataset. It serves as the baseline assumption to be tested and is typically expressed as an equality.

The null hypothesis is either rejected or not rejected based on evidence provided by sample data, using statistical tests.

Principles of Null Hypothesis :-

• Assumption of No Effect : The null hypothesis assumes no effect, no difference, or no relationship between variables.

• Basis for Comparison : It provides a baseline against which the alternative hypothesis (H_a) is evaluated.

• Testing Framework : The goal of hypothesis testing is to decide whether there is enough evidence in the data to reject H_0 in favor of H_a.

• Significance Level (α) : The null hypothesis is rejected if the test statistic falls in the critical region defined by α, often set to 0.05 (5%).

• Two Possible Outcomes :

  • Reject H_0 : Evidence is strong enough to support H_a.
  • Fail to Reject H_0 : Insufficient evidence to support H_a; H_0 remains plausible.

The formula for a test statistic depends on the type of test (e.g., Z-test, T-test, Chi-Square test). A common ge neral form is:

Test Statistic = (observed values - Expected value under H_0) / Standard Error

The calculated statistic is compared to critical values from the corresponding distribution to decide whether to reject H_0.

Hope it helps !

In probability and statistics, null hypothesis is a default status that there is zero or nothing happened. Principle of null hypothesis proposes that there is no significant differences or relationship between two variables. It serves as starting point or default assumption that there is no real change.

Formula for null hypothesis -

Null hypothesis formula (Ho) : parameter = value

Ho : u1 = u2