(c)Suppose the true mean lifetime of BIG's light bulbs is 3380 hours. Fill in the blanks to describe a Type II error. 

A Type II error would be rejecting/failing to reject the hypothesis that 

Let's fill in the blanks to describe a Type II error.

**Statement:**  
A Type II error would be **failing to reject** the hypothesis that the **mean lifetime of BIG's light bulbs is 3200 hours** when, in fact, the true mean lifetime is **3380 hours**.

So the full statement is:

**A Type II error would be failing to reject the hypothesis that the mean lifetime of BIG's light bulbs is 3200 hours when, in fact, the true mean lifetime is 3380 hours.**

Would you like to explore the probability of making a Type II error (known as beta, \( \beta \)), or any other details related to this scenario?

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**Related Questions:**

1. What factors influence the probability of making a Type II error?
2. How do you calculate the probability of a Type II error (\( \beta \))?
3. How does sample size affect the likelihood of a Type II error?
4. What is the relationship between Type I and Type II errors?
5. How do you calculate the power of a test (which is \( 1 - \beta \))?
6. What steps can be taken to reduce the likelihood of a Type II error?
7. How does the true mean (3380 hours) compare to the hypothesized mean in terms of effect size?
8. What role does the standard deviation of the sample play in hypothesis testing?

**Tip:** Always keep in mind that while minimizing Type I errors (false positives) is crucial, it should not come at the cost of drastically increasing the likelihood of Type II errors (false negatives). A balance is often required based on the context of the problem.

Explore the concept of Type II errors in hypothesis testing with a detailed explanation. Learn about the implications of failing to reject the hypothesis that the mean lifetime of BIG's light bulbs is 3200 hours when the true mean is 3380 hours. Discover factors influencing Type II errors and their relevance in statistical inference.

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