  We investigate the statistics of the available Pantheon+ dataset. Noticing
that the $\chi^2$ value for the best-fit $\Lambda$CDM model to the real data is
small, we quantify how significant its smallness is by calculating the
distribution of $\chi^2$ values for the best-fit $\Lambda$CDM model fit to mock
Pantheon+-like datasets, using the provided covariance matrix. We further
investigate the distribution of the residuals of the Pantheon+ dataset, with
respect to the best-fit $\Lambda$CDM model, and notice they scatter smaller
than would be expected from the covariance matrix but find no significant
amount of kurtosis. These results point to the conclusion that the Pantheon+
covariance matrix is over-estimated. One simple interpretation of these results
is a $\sim$5\% overestimation of errors on SN distances in Pantheon+ data. When
the covariance matrix is reduced by subtracting an intrinsic scatter term from
the diagonal terms of the covariance matrix, the best-fit $\chi^2$ for the
$\Lambda$CDM model achieves a normal value of 1580 and no deviation from
$\Lambda$CDM is detected. We further quantify how consistent the $\Lambda$CDM
model is with respect to the modified data with the subtracted covariance
matrix using model independent reconstruction techniques such as the iterative
smoothing method and we find that the standard model is consistent with the
data.
