stage Sleeping people who show theta waves on their EEGs are most likely in- sleep.

Theta waves are seen most prominently during stage 3 and stage 4 of the sleep cycle, which is also known as deep sleep. During these stages, the brain is generating significantly slower brain waves than during periods when a person is awake. This deep sleep is essential for rest and rejuvenation, as well as for allowing the body to heal and repair itself. It is also in this stage that vivid dreaming occurs, and the person may experience intense emotions or vivid imagery. It is very unlikely that someone would be showing theta waves on an EEG if they were in stage 1 or 2 of the sleep cycle, as those stages do not typically show theta wave activity. Similarly, REM sleep does not typically feature theta wave activity, so it is unlikely that someone showing theta waves on an EEG would be in REM. Therefore, the most likely stage for someone showing theta waves on an EEG would be stage 3 or 4 of the sleep cycle.