Questions: The power of a test is 0.981 . What is the probability of a Type II error?

The power of a test is 0.981 . What is the probability of a Type II error?
Transcript text: The power of a test is 0.981 . What is the probability of a Type II error?
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Solution

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Solution Steps

To find the probability of a Type II error, we need to understand the relationship between the power of a test and the probability of a Type II error. The power of a test is defined as \(1 - \beta\), where \(\beta\) is the probability of a Type II error. Therefore, to find \(\beta\), we can subtract the power from 1.

Step 1: Understanding the Power of a Test

The power of a statistical test is defined as the probability of correctly rejecting the null hypothesis when it is false. Mathematically, this is expressed as: \[ \text{Power} = 1 - \beta \] where \(\beta\) is the probability of a Type II error.

Step 2: Calculating the Probability of a Type II Error

Given that the power of the test is \(0.981\), we can rearrange the formula to find \(\beta\): \[ \beta = 1 - \text{Power} \] Substituting the given value: \[ \beta = 1 - 0.981 = 0.019 \]

Final Answer

The probability of a Type II error is \(\boxed{0.019}\).

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