A test is conducted at the alpha = 0.05 level of significance. What is the probability of a Type I error?

Verified step by step guidance

1. Understand the definition of a Type I error: it occurs when the null hypothesis is rejected even though it is actually true.
2. Recall that the significance level, denoted by \(\alpha\), is the threshold probability for rejecting the null hypothesis when it is true.
3. Recognize that the probability of making a Type I error is exactly equal to the significance level \(\alpha\).
4. Since the test is conducted at \(\alpha = 0.05\), the probability of a Type I error is \$0.05$.
5. Therefore, the probability of a Type I error is the same as the chosen significance level, which in this case is \$0.05$.

Key Concepts

Level of Significance (Alpha)

The level of significance, denoted by alpha (α), is the threshold probability set by the researcher for rejecting the null hypothesis. It represents the maximum acceptable risk of making a Type I error, commonly set at 0.05, meaning a 5% chance of incorrectly rejecting a true null hypothesis.

Type I Error

A Type I error occurs when the null hypothesis is true, but we mistakenly reject it. This error reflects a false positive result, and its probability is exactly equal to the chosen alpha level, indicating the risk of such an error in hypothesis testing.

Hypothesis Testing Framework

Hypothesis testing involves making decisions about population parameters based on sample data. It includes setting a null and alternative hypothesis, choosing a significance level, and determining whether to reject the null hypothesis based on test statistics and critical values.