Sleeping is an important activity to monitor since it has a crucial role in the overall health and well-being of the people and society. In order to diagnose the problems in sleep, different monitoring systems are developed in the literature. The unobtrusiveness, reduced cost, objectiveness, protection of privacy and user-friendliness are the main design considerations and the proposed system design achieves those objectives by utilizing smart wearables, smart watch and smart phone. The accelerometer and heart rate monitor sensors on smart watch and the sound level sensor on the smart phone are activated. The experiments with this system are performed with 17 subjects in a sleep clinic. The data collected from these subjects is used to generate various combinations by employing varied feature extraction, feature selection and sampling approaches. Five different machine learning algorithms are implemented and the classification results are generated using the various combinations of data, training and scoring strategies. The system performance is measured in two ways, the accuracy rate of distinguishing abnormal respiratory events is 85.95% and the classification success of subjects according to the problems in their respiration is one misclassification among 17 subjects. With all the methodology utilized in this study, the proposed system is a novel prescreening tool which recognizes the severity of problems in respiration during sleep.