Final answer:
Evidence supporting the claim that mobile games are what people do in their free time includes the high percentage of users who constantly check their phones, the fact that many sleep with their phones to not miss updates, and the tendency for leisure activities to be increasingly sedentary, focusing on mobile and computer-based entertainment.
Step-by-step explanation:
The textual evidence that best supports the statement about mobile games increasingly occupying our free time can be drawn from a few key pieces of data from the passage. First, research indicates that 67 percent of users check their phones for messages or calls even when the phone didn't ring, highlighting the prevalence of mobile device interaction. Furthermore, 44% of cell owners have slept with their phone next to their bed to not miss any updates during the night, signifying a strong attachment to mobile communication which can encompass gaming. Lastly, the observation that leisure activities have become more sedentary with an increase in activities such as computer games and web surfing suggests a trend toward the utilization of mobile games and technology during free time.