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Null Hypothesis

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

Examples:

  • The average height of women is equal to 160 cm. (H0: ฮผ = 160)
  • There is no relationship between exercise and blood pressure. (H0: ฯ = 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.

FAQs

  1. What is a null hypothesis?

    A null hypothesis (H0) is a statement that assumes no effect or no relationship between variables in a study. It is the default assumption to be tested.

  2. What should a null hypothesis include?

    A null hypothesis should clearly state that there is no significant effect or relationship between the variables being studied. It must be specific and testable.

  3. What is the difference between H0 and H1 in a hypothesis?

    H0 (null hypothesis) assumes no effect or relationship, while H1 (alternative hypothesis) proposes that there is a significant effect or relationship between the variables.

  4. What is the null hypothesis with an example?

    An example of a null hypothesis is: “There is no difference in test scores between students who study with music and those who study in silence.”

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