This is concept question, and is not based on your findings above.
Which of the following **two** statements regarding hypothesis test are FALSE?

Question 15Answer

There is a trade-off between the probability of Type I and the probability of Type II errors.

The null hypothesis is typically assumed to be true until there is sufficient statistical evidence to reject it

The smaller the significance level, the larger the probability of Type I error.

The higher the probability of Type I error, the higher the probability of Type II error.

To determine which of the two statements regarding hypothesis testing are false, let's analyze each statement:

1. **There is a trade-off between the probability of Type I and the probability of Type II errors.**
   - **True:** This statement is correct. When the significance level (α) is decreased, the probability of a Type I error (rejecting a true null hypothesis) decreases, but the probability of a Type II error (failing to reject a false null hypothesis) increases. This creates a trade-off between the two errors.

2. **The null hypothesis is typically assumed to be true until there is sufficient statistical evidence to reject it.**
   - **True:** This statement is also correct. In hypothesis testing, the null hypothesis (H₀) is assumed true, and the objective is to determine if there is enough evidence to reject it in favor of the alternative hypothesis (H₁).

3. **The smaller the significance level, the larger the probability of Type I error.**
   - **False:** This statement is incorrect. The significance level (α) directly represents the probability of a Type I error. A smaller significance level means a lower probability of making a Type I error, not a larger one.

4. **The higher the probability of Type I error, the higher the probability of Type II error.**
   - **False:** This statement is also incorrect. There is an inverse relationship between Type I and Type II errors. Increasing the probability of a Type I error (by increasing α) decreases the probability of a Type II error (β), and vice versa.

**The two false statements are:**
- **Statement 3:** "The smaller the significance level, the larger the probability of Type I error."
- **Statement 4:** "The higher the probability of Type I error, the higher the probability of Type II error."

Would you like more details or have any other questions? Here are some related questions:

1. What are the implications of increasing the sample size on Type I and Type II errors?
2. How do you choose an appropriate significance level for a hypothesis test?
3. What are some strategies to reduce both Type I and Type II errors?
4. Can you explain the consequences of Type I and Type II errors in real-world scenarios?
5. How does statistical power relate to Type II error?

**Tip:** Lowering the significance level reduces the risk of a Type I error but increases the risk of a Type II error, highlighting the importance of balancing the two based on the context of the test.

Explore the concepts of Type I and Type II errors in hypothesis testing. Learn about the trade-off between these errors, the significance level's impact, and strategies to minimize errors. Detailed analysis with examples.

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