In the context of hypothesis testing, when is there a risk of committing a ${\mathrm{Type}}^{\mathrm{I}}$ error?

• A. When the sample size is too small to detect an effect
• B. When the $H$₀ is actually false but is not rejected
• C. When the $H$₀ is actually true but is incorrectly rejected
• D. When the alternative hypothesis is true and is accepted

Answer: (C)

Verified step by step guidance

1. Understand the definition of a Type I error in hypothesis testing: it occurs when the null hypothesis, which is actually true, is incorrectly rejected.
2. Recall that the null hypothesis (denoted as \(H_0\)) represents the default or status quo assumption, while the alternative hypothesis (\(H_a\)) represents the claim we want to test.
3. Recognize that a Type I error is also known as a 'false positive' because it means detecting an effect or difference when none actually exists.
4. Note that the risk of committing a Type I error is controlled by the significance level \(\alpha\), which is the probability threshold set before the test to decide when to reject \(H_0\).
5. Therefore, the risk of a Type I error arises specifically when \(H_0\) is true but the test results lead us to reject it mistakenly.