Mel-frequency cepstral coefficients (MFCCs) are an important feature in speech processing. A deeper understanding of their properties can contribute to the work that is being done with both classical and deep learning models. This study challenges the long-held assumption that MFCCs lack relevant temporal information by investigating their relationship with speech prosody. Using a null hypothesis significance testing framework, a systematic assessment is made about the statistical independence between MFCCs and the three prosodic features: energy, fundamental frequency (F0), and voicing. The results demonstrate that it is statistically implausible that the MFCCs are independent of any of these three prosodic features. This finding suggests that MFCCs inherently carry valuable prosodic information, which can inform the design of future models in speech analysis and recognition.