A researcher is conducting a statistical hypothesis test. The alpha level (a) is set to .05 and the statistical power is .80. What is the probability of making a Type II error? O.95 .80 .20 O.05
A researcher is conducting a statistical hypothesis test. The alpha level (a) is set to .05 and the statistical power is .80. What is the probability of making a Type II error? O.95 .80 .20 O.05
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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![### Understanding Hypothesis Testing: Type I and Type II Errors
A researcher is conducting a statistical hypothesis test. The alpha level (α) is set to 0.05 and the statistical power is 0.80. What is the probability of making a Type II error?
**Multiple Choice Options:**
- O 0.95
- O 0.80
- O 0.20
- O 0.05
### Explanation:
In the context of hypothesis testing, two types of errors can occur:
- **Type I Error (α)**: This is the error of rejecting a true null hypothesis. The symbol α represents the probability of making a Type I error, which is given as 0.05 (5%) in this scenario.
- **Type II Error (β)**: This is the error of failing to reject a false null hypothesis. The statistical power of a test is defined as 1 - β. The power of the test is provided as 0.80 (80%) in this case.
To find the probability of making a Type II error (β), we can use the relationship between power and β:
\[ \text{Power} = 1 - \beta \]
Given that the statistical power is 0.80, we can solve for β:
\[ 0.80 = 1 - \beta \]
\[ \beta = 1 - 0.80 \]
\[ \beta = 0.20 \]
Therefore, the probability of making a Type II error in this scenario is 0.20 (20%). The correct answer is the third option:
- O 0.20](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7a520971-fd90-49dd-bfdc-9027208d76cd%2F4601c408-e0cf-49d1-aa63-54e039216d2e%2F4mfxwfb_processed.png&w=3840&q=75)
Transcribed Image Text:### Understanding Hypothesis Testing: Type I and Type II Errors
A researcher is conducting a statistical hypothesis test. The alpha level (α) is set to 0.05 and the statistical power is 0.80. What is the probability of making a Type II error?
**Multiple Choice Options:**
- O 0.95
- O 0.80
- O 0.20
- O 0.05
### Explanation:
In the context of hypothesis testing, two types of errors can occur:
- **Type I Error (α)**: This is the error of rejecting a true null hypothesis. The symbol α represents the probability of making a Type I error, which is given as 0.05 (5%) in this scenario.
- **Type II Error (β)**: This is the error of failing to reject a false null hypothesis. The statistical power of a test is defined as 1 - β. The power of the test is provided as 0.80 (80%) in this case.
To find the probability of making a Type II error (β), we can use the relationship between power and β:
\[ \text{Power} = 1 - \beta \]
Given that the statistical power is 0.80, we can solve for β:
\[ 0.80 = 1 - \beta \]
\[ \beta = 1 - 0.80 \]
\[ \beta = 0.20 \]
Therefore, the probability of making a Type II error in this scenario is 0.20 (20%). The correct answer is the third option:
- O 0.20
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