Recent decade has seen great progress in the use of stochastic models in biological process. Researchers are now realising that stochastic models have important roles to play in biological process especially in the analysis of population dynamics. This progress encourages many researchers to develop new methods and techniques to improve the stochastic model. In recent study, logistic equations have been used to model the cell growth of C. acetobutylicum while the Luedeking-Piret equation incorporating the logistic equation used to model the formation of solvent. However, it was found that the Luedeking-Piret equation is not adequate for modeling the production of acetone and butanol. In this study, stochastic power law logistic model has been considered to model the cell growth of C. acetobutylicum and the solvent production in five different yeast cultures. In order to solve the SDEs, simulated maximum likelihood estimation method and Euler-Maruyama approximation method have been used. Finally, the stochastic models and deterministic models are compared by using their root mean square errors of the growth model and solvent productions model. The stochastic models have smaller value of root mean square errors, thus showed that the stochastic power law logistic models are better models than their deterministic counterparts to describe the growth of C. acetobutylicum and solvent productions in fermentation.