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Answer: The probability of committing a Type II error decreases when the sample size increases and the level of significance is held constant.
## Explanation Let's analyze each option: **Option A: CORRECT** - Type II error (β) occurs when we fail to reject a false null hypothesis (accepting a bad model) - As sample size increases while significance level (α) remains constant, the statistical power (1-β) increases - This means the probability of Type II error (β) decreases with larger sample sizes **Option B: INCORRECT** - Statistical power is defined as 1 - β (probability of Type II error) - However, there's a trade-off between Type I and Type II errors - A test cannot minimize Type II error "regardless" of Type I error probability - Reducing Type II error typically increases Type I error risk **Option C: INCORRECT** - Type I error (α) occurs when we reject a true null hypothesis (rejecting a good model) - This option describes Type II error, not Type I error **Option D: INCORRECT** - Type II error (β) occurs when we fail to reject a false null hypothesis (accepting a bad model) - This option describes Type I error, not Type II error **Key Definitions:** - **Type I Error (α)**: Rejecting a true null hypothesis (false positive) - **Type II Error (β)**: Failing to reject a false null hypothesis (false negative) - **Statistical Power (1-β)**: Probability of correctly rejecting a false null hypothesis In backtesting context: - Type I: Rejecting a correctly specified VaR model - Type II: Accepting an incorrectly specified VaR model
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A model validation team at a bank is backtesting the bank's VaR model. In preparation for the backtest, one of the team members expresses a concern that the validation process could result in the team committing a Type I error or a Type II error and discusses the characteristics of these errors with the team. Which of the following is correct regarding Type I and Type II errors?
A
The probability of committing a Type II error decreases when the sample size increases and the level of significance is held constant.
B
A backtest is considered statistically powerful if it minimizes the probability of committing a Type II error regardless of the probability of committing a Type I error.
C
A Type I error is committed when an incorrectly specified model is accepted.
D
A Type II error is committed when a correctly specified model is rejected.