Hypothesis Testing WS # 1

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What is a null hypothesis (H₀)?

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The null hypothesis (H₀) is a statement that there is no effect or no difference, and it serves as the default assumption in hypothesis testing.

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What is an alternative hypothesis (H₁ or Hₐ)?

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The alternative hypothesis (H₁ or Hₐ) is a statement that indicates the presence of an effect or a difference, opposing the null hypothesis.

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How do you state a hypothesis for a proportion?

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A hypothesis for a proportion is stated in the form H₀: p = p₀ for the null hypothesis and H₁: p ≠ p₀, p < p₀, or p > p₀ for the alternative hypothesis, where p is the true proportion.

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What does it mean to test if a proportion is less than a certain value?

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Testing if a proportion is less than a certain value involves formulating a hypothesis where the alternative hypothesis states H₁: p < p₀, indicating that the true proportion is less than the specified value.

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What does it mean to test if a proportion is greater than a certain value?

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Testing if a proportion is greater than a certain value involves formulating a hypothesis where the alternative hypothesis states H₁: p > p₀, indicating that the true proportion is greater than the specified value.

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What does it mean to test if a proportion is different from a certain value?

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Testing if a proportion is different from a certain value involves formulating a hypothesis where the alternative hypothesis states H₁: p ≠ p₀, indicating that the true proportion is not equal to the specified value.

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What is the significance level (α) in hypothesis testing?

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The significance level (α) is the probability of rejecting the null hypothesis when it is actually true, commonly set at 0.05 or 0.01.

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What is a p-value in hypothesis testing?

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A p-value is the probability of obtaining test results at least as extreme as the observed results, assuming that the null hypothesis is true.

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What does it mean if the p-value is less than the significance level?

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If the p-value is less than the significance level (α), it indicates strong evidence against the null hypothesis, leading to its rejection.

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What is a Type I error in hypothesis testing?

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A Type I error occurs when the null hypothesis is rejected when it is actually true.