Past exam of the mathematics course of the University of Cambridge / 2019 / ib / Paper 3 / 20H / c

Let $z_p$ denote the $p$-quantile of the standard normal distribution. Since the variance is known,so a $100(1-\alpha )\%$ confidence interval is

Let $t_{\nu ,p}$ denote the $p$-quantile of Student's t-distribution. Part (b) gives the Student t confidence interval

Let ${\chi }_{\nu ,p}^2$ denote the $p$-quantile of the chi-squared distribution. Since $S_{XX}/{\sigma }^2\sim {\chi }_{n-1}^2$, inversion of the central probability event givesas a $100(1-\alpha )\%$ confidence interval for ${\sigma }^2$.