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Contrary to expectations that the coronavirus pandemic would terminate quickly, the number of people infected with the virus did not decrease worldwide and coronavirus-related deaths continue to occur every day. The standard COVID-19 diagnostic test technique used today, PCR testing, requires professional staff and equipment, which is expensive and takes a long time to produce test results. In this paper, we propose a feature set consisting of four features: MFCC, Δ²-MFCC, Δ-MFCC, and spectral contrast as a feature set optimized for the diagnosis of COVID-19, and apply it to a model that combines ResNet-50 and DNN. Crowdsourcing datasets from Cambridge, Coswara, and COUGHVID are used as the cough sound data for our study. Through direct listening and inspection of the dataset, audio recordings that contained only cough sounds were collected and used for training. The model was trained and tested using cough sound features extracted from crowdsourced cough data and had a sensitivity and specificity of 0.95 and 0.96, respectively.