Fix the mistake: Statistical Inference ④ (Hypothesis Testing)

What Is Hypothesis Testing?

Hypothesis testing is a method of using sample data to judge whether an assumption about a population is correct.

  • Null hypothesis H₀: the hypothesis to be rejected (for example, “there is no effect”)
  • Alternative hypothesis H₁: the hypothesis to be supported (for example, “there is an effect”)
  • Significance level α: the upper limit on the probability of incorrectly rejecting H₀ (usually 5% or 1%)
Example ① We want to test the effectiveness of a new drug. What are H₀ and H₁?
Solution:H₀: no effect; H₁: effect exists
Key Point
  • “Reject H₀” ⇔ accept H₁

Practice Problems

  1. What are the null and alternative hypotheses for testing whether a coin is “fair”?

Solutions and Explanations

  1. Solution:H₀：p=1/2 (fair), H₁：p≠1/2 (biased)

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