This was in an past exam question I came across.

A first-order autoregressive model has been fitted to a time series of 50 observations giving $\hat\mu = 15$ and $\hat\alpha =0.6$.

The first 12 residual autocorrelations were given and the estimated standard deviation of $r_k(Z_t)=0.15$. The question was to check the adequacy of the fitted model. The only adequacy test we were given was the Ljung-Box test which I think uses sample autocorrelations, not residual autocorrelations.