Exercise 4:
Let $X_1, \dots, X_N$ be i.i.d. and normally distributed. This means $X_n \sim \mathcal{N}(\mu, \sigma^2)$, with $\mu \in \mathbb{R}$ unknown and $\sigma^2 \in \mathbb{R}^+$ known.
a) Determine the two-sided confidence interval for the level of significance $\gamma$ and $\mu$. How does this confidence interval change, if the sample size $N$ or the level of significance $\gamma$ increases? Give an explanation of these two changes.
b) Determine an one-sided confidence interval for the level of significance 0.95. How does this confidence interval change, if the sample size $N$ or the significance level $\gamma$ increases? Give an explanation of these two changes.
