Questions: A type I error occurs when the null hypothesis is rejected when it is true.

A type I error occurs when the null hypothesis is rejected when it is true.
Transcript text: A type I error occurs when the null hypothesis is rejected when it is true.
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Solution

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Solution Steps

Step 1: Definition of Type I Error

A Type I error occurs when the null hypothesis (\(H_0\)) is rejected when it is actually true. This situation leads us to conclude that there is an effect or difference when, in fact, there is none.

Mathematically, this can be expressed as:

  • Reject \(H_0\) when \(H_0\) is true.
Step 2: Implications of Type I Error

The implications of committing a Type I error are significant in hypothesis testing. It is also referred to as a "false positive" or "alpha error." The probability of making a Type I error is denoted by the significance level (\(\alpha\)), which is typically set at values like \(0.05\) or \(0.01\).

Final Answer

The answer is that a Type I error occurs when the null hypothesis is rejected when it is true. This is also known as a "false positive" or "alpha error."

\(\boxed{\text{Type I error: Reject } H_0 \text{ when } H_0 \text{ is true}}\)

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