By How Much Must the Sample Size N Be Increased $\left( \bar { x } \pm z _ { \alpha n } \cdot \frac { \sigma } { \sqrt { n } } \right)$

Essay

By how much must the sample size n be increased if the width of the CI $\left( \bar { x } \pm z _ { \alpha n } \cdot \frac { \sigma } { \sqrt { n } } \right)$ is to be halved? If the sample size is increased by a factor of 25, what effect will this have on the width of the interval? Justify your assertions.