Statistical analysis of Blind source separation problem has remained the main focus of mathematician and Engineers for the past two decades in diverse fields of science. The popular data mining technique of principle component analysis and fast revolutionary method of independent component analysis (ICA) has been deployed here as a solution to the above mentioned problem. Our contribution outlines the performance of these two statistical analysis tools in the case of super-gaussian linear noisy speech signal mixtures. Speech signals were mixed in the presence of noise and then these artificial noisy speech data were separated using the eigenvalue decomposition algorithm of PCA and a novel algorithm of ICA based on the mathematical model of PCA and ICA. The quality of separated speech signals were comparatively evaluated using the SNR of each signal. All the visual and analytical results suggest that ICA retrieve all the independent components more faithfully than PCA in our noisy speech signals scenario.