Probability of exceptions

NO.PZ2023100703000036问题如下 Basel II requires a backtest of a bank’s internvalue risk (VaR) mol (IMA). Assume the bank’s ten-y 99% Vis $1 million (minimum of 99% is harwireper Basel). The null hypothesis is: the Vmol is accurate. Out of 1,000 observations, 25 exceptions are observe(we sthe actuloss exceethe V25 out of 1000 observations).A.We will probably call the Vmol goo(accurate) but we risk a Type I error.B.We will probably call the Vmol goo(accurate) but we risk a Type II error.C.We will probably call the mol b(inaccurate) but we risk a Type I error.We will probably call the mol b(inaccurate) but we risk a Type II error.The probability of 25 or more exceptions will only observe1 – 99.996%. So, we rejethe mol. Null = goomol. To ci the mol is bmol is to rejenull anthis implies a risk of type I error.为什么拒绝了原假设反而会犯一类错误，一类错误不是接受错误的假设么

NO.PZ2023100703000036 问题如下 Basel II requires a backtest of a bank’s internvalue risk (VaR) mol (IMA). Assume the bank’s ten-y 99% Vis $1 million (minimum of 99% is harwireper Basel). The null hypothesis is: the Vmol is accurate. Out of 1,000 observations, 25 exceptions are observe(we sthe actuloss exceethe V25 out of 1000 observations). A.We will probably call the Vmol goo(accurate) but we risk a Type I error. B.We will probably call the Vmol goo(accurate) but we risk a Type II error. C.We will probably call the mol b(inaccurate) but we risk a Type I error. We will probably call the mol b(inaccurate) but we risk a Type II error. The probability of 25 or more exceptions will only observe1 – 99.996%. So, we rejethe mol. Null = goomol. To ci the mol is bmol is to rejenull anthis implies a risk of type I error. 如何判断的1-99.996%处于拒绝域内啊，题目也没给置信水平呀

NO.PZ2023100703000036 问题如下 Basel II requires a backtest of a bank’s internvalue risk (VaR) mol (IMA). Assume the bank’s ten-y 99% Vis $1 million (minimum of 99% is harwireper Basel). The null hypothesis is: the Vmol is accurate. Out of 1,000 observations, 25 exceptions are observe(we sthe actuloss exceethe V25 out of 1000 observations). A.We will probably call the Vmol goo(accurate) but we risk a Type I error. B.We will probably call the Vmol goo(accurate) but we risk a Type II error. C.We will probably call the mol b(inaccurate) but we risk a Type I error. We will probably call the mol b(inaccurate) but we risk a Type II error. The probability of 25 or more exceptions will only observe1 – 99.996%. So, we rejethe mol. Null = goomol. To ci the mol is bmol is to rejenull anthis implies a risk of type I error. 假设检验可以让我们拒绝了一个原本错误的假设，这什么错误也没范啊

NO.PZ2023100703000036问题如下 Basel II requires a backtest of a bank’s internvalue risk (VaR) mol (IMA). Assume the bank’s ten-y 99% Vis $1 million (minimum of 99% is harwireper Basel). The null hypothesis is: the Vmol is accurate. Out of 1,000 observations, 25 exceptions are observe(we sthe actuloss exceethe V25 out of 1000 observations).A.We will probably call the Vmol goo(accurate) but we risk a Type I error.B.We will probably call the Vmol goo(accurate) but we risk a Type II error.C.We will probably call the mol b(inaccurate) but we risk a Type I error.We will probably call the mol b(inaccurate) but we risk a Type II error.The probability of 25 or more exceptions will only observe1 – 99.996%. So, we rejethe mol. Null = goomol. To ci the mol is bmol is to rejenull anthis implies a risk of type I error.99% confinlevel就是1000个里面有10个exception，跟实际的25个相比，说明实际的confinlevel得是97.5%。那实际发生的有一部分本应该accept的被视为reject，也就是type I error变大，这样理解对不