Explanation

Let's analyze each option:

Option A: "Type II error refers to the failure to reject the H₁ when it is actually false." - This is incorrect. Type II error is the failure to reject the null hypothesis (H₀) when it is actually false, not H₁.

Option B: "Hypothesis testing is used to make inferences about the parameters of a given population on the basis of statistics computed for a sample that is drawn from another population." - This is incorrect. Hypothesis testing uses a sample drawn from the same population, not from another population.

Option C: "All else being equal, the decrease in the chance of making a Type I error comes at the cost of increasing the probability of making a Type II error." - This is correct. There is a trade-off between Type I and Type II errors. When we decrease the significance level (α) to reduce Type I errors, we increase the probability of Type II errors (β).

Option D: "If the p-value is greater than the significance level, then the statistics falls into the reject intervals." - This is incorrect. When the p-value is greater than the significance level, we fail to reject the null hypothesis, meaning the test statistic does NOT fall into the rejection region.

Key Concepts:

• Type I Error (α): Rejecting H₀ when it is actually true
• Type II Error (β): Failing to reject H₀ when it is actually false
• Trade-off: Decreasing α increases β, and vice versa
• p-value interpretation: p-value < α → reject H₀; p-value ≥ α → fail to reject H₀