You are testing a hypothesis at 𝛼 = 0.01. What is the probability of committing a Type I error?*99%10%1%0%None of the above
Question
You are testing a hypothesis at 𝛼 = 0.01. What is the probability of committing a Type I error?
- 99%
- 10%
- 1%
- 0%
- None of the above
Solution
Step 1: Break Down the Problem
To solve the problem, we need to understand what a Type I error is in hypothesis testing. A Type I error occurs when we reject the null hypothesis when it is, in fact, true. The significance level, denoted by , represents the probability of committing a Type I error.
Step 2: Relevant Concepts
In this case, the significance level has been given as 0.01. This represents the threshold at which we determine whether to reject the null hypothesis.
Step 3: Analysis and Detail
Since is defined as the probability of committing a Type I error, if , then the probability of committing a Type I error is simply 1% or 0.01.
Step 4: Verify and Summarize
Given the direct relationship between and the probability of a Type I error, our findings verify that the probability of committing a Type I error is indeed equal to the given significance level.
Final Answer
The probability of committing a Type I error is .
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