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In late November 2020, there was a flurry of media coverage of two companies’ claims of 95% efficacy rates of newly developed COVID-19 vaccines, but information about the confidence interval was not reported. This paper presents a way of teaching the concept of hypothesis testing and the construction of confidence intervals using numbers announced by the drug makers Pfizer and Moderna publicized by the media. Instead of a two-sample test or more complicated statistical models, we use the elementary one-proportion z -test to analyze the data. The method is designed to be accessible for students who have only taken a one-semester elementary statistics course. We will justify the use of a z -distribution as an approximation for the confidence interval of the efficacy rate. Bayes’s rule will be applied to relate the probability of being in the vaccine group among the volunteers who were infected by COVID-19 to the more consequential probability of being infected by COVID-19 given that the person is vaccinated.