The null hypothesis is a statement that there is no difference or no relationship between two variables or groups. It is a statement of no effect or no difference, which is assumed to be true unless proven otherwise.

Symbolic Notation:

H0: p = 0

where:

• H0 is the null hypothesis
• p is the population parameter being tested
• 0 represents the hypothesized value of p (usually zero)

Types of Null Hypotheses:

• Directional: Specifies the direction of the expected effect (e.g., H0: μ > 50).
• Non-directional: Does not specify the direction of the expected effect (e.g., H0: μ = 50).
• Two-tailed: Tests for difference in either direction from the hypothesized value (e.g., H0: μ = 50).
• One-tailed: Tests for difference in only one direction from the hypothesized value (e.g., H0: μ > 50).

Examples:

• The average height of women is equal to 160 cm. (H0: μ = 160)
• There is no relationship between exercise and blood pressure. (H0: ρ = 0)
• The probability of winning a lottery is 0.05. (H0: p = 0.05)

Importance:

• Null hypotheses are essential for statistical testing.
• They provide a clear statement of the hypothesis to be tested.
• Null hypotheses are used to guide the selection of appropriate statistical tests.
• They help interpret the results of statistical tests and draw conclusions.

Note:

• Null hypotheses are not necessarily true. They are assumptions that need to be tested against evidence.
• If the null hypothesis is rejected, it does not necessarily mean that the alternative hypothesis is true.