I came across this problem in my self-study. I found a solution with the help from this forum (answer below) and posted my solution here.

Assume that $X\_i$, $i\in\mathbb N$ is a sequence of I.I.D. random variables
with a mean $\mu \neq 0$ and variance $\sigma^2$.
We want to estimate $\dfrac{1}{\mu^2}$ using $\dfrac{1}{\overline X^2}$.

* Write the formula for confidence interval for $\mu$, say $(c\_1, c\_2)$.
* Write the formula for confidence interval for $\dfrac{1}{\mu^2}$, say $(d\_1, d\_2)$.
* Do we have $(\dfrac{1}{c\_1^2},\dfrac{1}{ c\_2^2})$=$(d\_1, d\_2)$

Would appreciate any constructive critique!