Brain Computer Interface systems provide the tools for translating raw acquired brain signals into commands to control an application or a device. Advancement in bio- medical signal processing techniques has directed the Electroencephalography (EEG) signals not only as a diagnostic tool for brain disease, but also as a controller in the field of Brain Computer Interface (BCI). In this paper, we present an EEG data analysis to study how EEG activity changes with right and left imagery hand movements as a step toward how humans can control machines using their thoughts. In this paper, power spectrum, event related potential and time frequency analysis showed that an imagination of right hand causes a decrease in activity in the hand area of sensory motor cortex in the left side of the brain and an imagination of left hand cause a decrease in activity in the hand area of sensory motor cortex in the right side of the brain.