I am given a sample size of 9 from a normal population, as well as the 95% confidence interval for population mean. I want to calculate the 95% population variance.

I see that the confidence interval for an unknown population mean is $\overline{Y}\pm {t}_{\frac{\alpha}{2}}\frac{S}{\sqrt{n}}$. Then since the midpoint of the confidence interval for population mean is the sample mean, I can plug that into $\overline{Y}$, 9 into n, and 0.025 into $\alpha $. From there, I can solve for S. How can I find the confidence interval for population variance from there?