When a biased estimator wins

You estimate a signal's mean $\mu$ from a single noisy reading $X$ with $E[X]=\mu$ and $\operatorname{Var}(X)=16$. The true value happens to be $\mu=4$. Compare two estimators by mean-squared error: the unbiased $\hat\mu_1=X$, and the shrink-toward-zero $\hat\mu_2=\tfrac12 X$. What is the MSE of the better estimator?