This study focused on the growing phenomenon of relationships with social AI agents and investigated the impact of these relationships on human relationships. One hundred and eighty-three participants were randomly assigned to either converse with a social AI chatbot or play a text-based word game for 21 days. Changes in participants' social health and relationships were tracked through four surveys and two audio-recorded interviews. The study found that the 21-day interactions with the chatbot did not significantly impact participants' social health or relationships compared to the control group. However, individuals with a high need for social connection tended to anthropomorphize the chatbot more. Those who anthropomorphized the chatbot more reported that their interactions with the chatbot had a greater impact on their social interactions with family and friends. The results suggest that the impact of human-AI interactions on human-human social outcomes is mediated by the degree to which people anthropomorphize the AI agent, which in turn is related to their need for social connection.