terms, i.e., $C=0$. In each case, we fixed the previously best-fit parameters: $A, B, C, \gamma, \theta_{\mbox{\tiny FIT}}$, and $\sigma_{\mbox{\tiny FIT}}$, and calculated the $\chi^2$ amplitude for each value $\alpha$. This was performed in the range $0.25 \le \theta \le 3.5^{\circ}$ and for $0.7 \le \alpha \le 1.2$.

We show in figure \[fig3\] the $\chi^2$ vs. $\alpha$ curves for $C = 0$ (red curve) and $C \neq 0$ (black curve), where $\Delta\chi^2(\alpha) = \chi^2(\alpha) - \chi^2_{min}$, with $\chi^2_{min}$ being the minimum $\chi^2$ value for $C \neq 0$. The difference between the two $\Delta\chi^2$ curves at $\alpha = \alpha_{min}$, for which the black line attain its minimum value, $\chi^2(\alpha_{min}) = \chi^2_{min}$, provides the statistical significance of the BAO measurement. As illustrated in figure \[fig3\], for $N_{\mbox{\scriptsize b}} = 29$ and using the non-linear covariance matrix, with a difference of 4.48 between the red and black curves at $\alpha_{min} = 0.9796$, the BAO detection significance is $2.12 \, \sigma$ (i.e., 97% confidence level). A summary of the statistical significances estimated for different $N_{\mbox{\scriptsize b}}$ values and diverse error estimation methods is presented in Table \[table1\]; it also includes the jackknife and bootstrap estimators.

![image](figure3)

   Error methods $\backslash$ $N_{\rm b}$        29             33             35       
  