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In the absence of pharmaceutical interventions to curb the spread of COVID-19, countries relied on a number of nonpharmaceutical interventions to fight the first wave of the pandemic. The most prevalent one has been stay-at-home orders, whose the goal is to limit the physical contact between people, which consequently will reduce the number of secondary infections generated. In this work, we use a detailed set of mobility data to evaluate the impact that these interventions had on alleviating the spread of the virus in the US as measured through the COVID-19-related deaths. To establish this impact, we use the notion of Granger causality between two time-series. We show that there is a unidirectional Granger causality, from the median percentage of time spent daily at home to the daily number of COVID-19-related deaths with a lag of 2 weeks. We further analyze the mobility patterns at the census block level to identify which parts of the population might encounter difficulties in adhering and complying with social distancing measures. This information is important, since it can consequently drive interventions that aim at helping these parts of the population.