If we do not reject the null hypothesis when the statement in the alternative hypothesis is true, we have made a Type ________ error.

Verified step by step guidance

1. Recall the definitions of Type I and Type II errors in hypothesis testing:
2. A Type I error occurs when we reject the null hypothesis \(H_0\) even though it is true.
3. A Type II error occurs when we fail to reject the null hypothesis \(H_0\) even though the alternative hypothesis \(H_a\) is true.
4. In this problem, since we do not reject \(H_0\) when the alternative hypothesis is true, this corresponds to a Type II error.
5. Therefore, the blank should be filled with "II" to indicate a Type II error.

Key Concepts

Null Hypothesis (H0)

The null hypothesis is a default assumption that there is no effect or difference in a population. It serves as the starting point for statistical testing, and we either reject or fail to reject it based on sample data.

Alternative Hypothesis (H1)

The alternative hypothesis represents a statement that contradicts the null hypothesis, suggesting that there is an effect or difference. It is what researchers aim to support through evidence from data.

Type II Error (False Negative)

A Type II error occurs when we fail to reject the null hypothesis even though the alternative hypothesis is true. This means missing a real effect or difference, often due to insufficient sample size or low test power.