Cognitive Impairment, commonly termed as Dementia, affects a large number of older adults. People with dementia (PwD) experience cognitive decline that impacts their ability to perform daily activities and maintain social connections. The number of PwD is expected to rise, and unfortunately, there is still no cure. A number of non drug therapies such as music and art therapy are used to stimulate neurons and slow down the progress of the disease. When symptoms become severe, full-time care may be needed, requiring a move to a nursing home for formal care. However, studies show that interaction with peers is limited in a care home, leading to loneliness and reduced quality of life. Caregivers organize group activities like singing and baking to alleviate these feelings, but their busy schedule can limit the frequency of these exercises. This begs the question: Can a robot support caregivers in the provision of group activities in a care home? This would allow caregivers more time to attend to the personal needs of the residents. It not only has the potential to reduce workload of caregivers but also creates opportunities for residents to interact with each other. In this thesis, we propose the design of a robot which moderates a sing-along activity for a group of people living in a nursing home. An activity in the realm of music therapy is chosen since it is one of the non-drug therapies which has shown to have numerous benefits like improving memory recall, eliciting emotions and aiding relaxation. The robot session is curated to give opportunities for interaction with group members and with the robot too. While the song is playing and participants are singing along with the music, the robot performs engagement detection, and encourages those who do not seem involved. Multiple ways are proposed to detect engagement in HRI, such as emotion recognition and estimation of head pose. These approaches have limitations in the scope of this thesis, particularly because these methods are not designed for groups of older adults residing in a care home. Given these limitations and our focus on the target group, we propose a novel engagement detection methodology, which leverages the presence of a robot and assigns an active role to it. Instead of relying on conventional passive engagement detection methods, this approach uses an interactive probing technique. The robot prompts users to perform certain actions, and whether or not they respond to it is monitored using pose estimation. This is termed robot engagement. This approach is combined with activity engagement, which indicates whether the participant is singing or not. With this hybrid technique, we aim to increase the efficacy of engagement detection. If a participant is detected as disengaged, either in the activity or in the robot, we provide personalized encouragement and motivation by addressing participants by name. Along with this, the robot also compliments those who actively participate, motivating them further...