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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 **Option A is correct** because as the sample size increases, the confidence region for the failure rate (expressed as N/T) of a correctly specified model shrinks. This makes it easier to detect and reject incorrectly specified models, thereby reducing the probability of Type II errors (failing to reject a false null hypothesis) while holding the significance level constant. **Option B is incorrect** because a statistically powerful test minimizes both Type I and Type II errors, not just Type II errors regardless of Type I errors. The power of a test is defined as 1 - P(Type II error), but this must be considered in conjunction with controlling Type I error rates. **Option C is incorrect** because a Type I error occurs when we **reject** a correctly specified model (false positive), not when we accept an incorrectly specified model. **Option D is incorrect** because a Type II error occurs when we **fail to reject** an incorrectly specified model (false negative), not when we reject a correctly specified model. ### Key Definitions: - **Type I Error**: Rejecting a true null hypothesis (rejecting a correctly specified model) - **Type II Error**: Failing to reject a false null hypothesis (accepting an incorrectly specified model) - **Statistical Power**: The probability of correctly rejecting a false null hypothesis (1 - P(Type II error))
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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.