Suppose we have an estimate ($\bar{y}$) and want to generate a confidence interval. However, we only have the variance of the sampling distribution ($v$) - and not the $\text{n}$.

Instead of:

$$
CI(\bar{Y})=\bar{Y}\pm(1.96)\*SE
$$

Could we use the SD instead since we only have the variance and can't find the SE, like this:

$$
CI(\bar{Y})=\bar{Y}\pm(1.96)\*\sqrt{v}
$$

Is this appropriate since we can't find the SE without knowing the n? Our interpretation would change due to focusing on variability between samples and not within a single sample, but is this the only approach with that limited information to creating a confidence interval?

Thanks