Math Problem Statement

Which of the following is NOT a true statement about error in hypothesis testing? Choose the correct answer out of the 4 options : A) a type I error is making the mistake of rejecting the null hypothesis when it is actually false B) a type II error is making the mistake of failing to reject the null hypothesis when it is actually false C)

Solution

The question seems incomplete, but from the given options, I can provide insight on the nature of Type I and Type II errors in hypothesis testing. Let’s examine the two options presented:

  • Option A: "A Type I error is making the mistake of rejecting the null hypothesis when it is actually false."

    • This is incorrect because a Type I error occurs when we reject the null hypothesis when it is actually true, not false. This is also referred to as a "false positive."
  • Option B: "A Type II error is making the mistake of failing to reject the null hypothesis when it is actually false."

    • This is correct, as a Type II error occurs when we fail to reject the null hypothesis when it is actually false. This is also known as a "false negative."

Since Option A is incorrect, it is likely the answer.

If you'd like the remaining two options completed or further clarification on hypothesis testing, let me know!


Do you have any further questions, or would you like more details on hypothesis testing?

Here are five questions that build on this topic:

  1. What are some examples of real-life applications of Type I and Type II errors?
  2. How does the significance level (α\alpha) relate to the probability of Type I error?
  3. What is the relationship between sample size and Type II error?
  4. How can we minimize both Type I and Type II errors in a hypothesis test?
  5. What is the power of a test, and how is it related to Type II error?

Tip: Reducing Type I errors usually increases the risk of Type II errors, and vice versa. Balancing both is crucial in hypothesis testing.

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Math Problem Analysis

Mathematical Concepts

Hypothesis Testing
Type I Error
Type II Error

Formulas

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Theorems

Concepts of Type I and Type II errors in hypothesis testing

Suitable Grade Level

Grades 10-12