Math Problem Statement

leo rejects the null hypothesis when, in fact , it is true. what type of error is leo committing?

Solution

Leo is committing a Type I error.

A Type I error occurs when a hypothesis test incorrectly rejects the null hypothesis when it is actually true. In other words, it’s a false positive — concluding that there is an effect or difference when there is none.

To summarize:

  • Type I error (false positive): Rejecting the null hypothesis when it is true.
  • Type II error (false negative): Failing to reject the null hypothesis when it is false.

Would you like more details on hypothesis testing or Type I and Type II errors?

Here are some related questions:

  1. What are the consequences of committing a Type I error in hypothesis testing?
  2. How can we control the probability of a Type I error (α)?
  3. What is the significance level (α) in hypothesis testing, and how does it relate to errors?
  4. How can you detect a Type II error in a hypothesis test?
  5. What are common methods to reduce Type I and Type II errors?

Tip: To minimize Type I errors, you can reduce the significance level (α), but this may increase the risk of a Type II error. Balancing both is key.

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Math Problem Analysis

Mathematical Concepts

Hypothesis Testing
Type I Error
Type II Error

Formulas

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Theorems

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Suitable Grade Level

Grades 11-12