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 givving $ \mu $ (hat) =15 and $\alpha$ (hat)=0.6

Then the first 12 residual autocorrelations were given and that the estimated standard deviation of $r_k(Z_t)$=0.15 and was asked to check the adequacy of the fitted model. The only adequacy test we were given was the Ljung Box test which I thin uses sample autocorrelations not residual autocorrelation. Please help me how to solve this any help would be appreciated.