Using software to teach statistical inference in introductory courses opens the door for methods and practices that are more conceptually appealing to students. With an increasing number of fields requiring competency in statistics including data science, natural and social sciences, public health and more, it is crucial that we as instructors deliver the basic concepts of statistics effectively. In line with guidelines presented in the GAISE College Report, this article demonstrates intuitive approaches to teaching proportion and mean inference that take advantage of statistical software and emphasize conceptual understanding. The article recommends putting aside asymptotic-based methods for proportion inference and using the exact binomial method. Regarding mean inference, we propose a more contextualized and simplified process that uses the distribution of the sample mean directly and avoids standardized statistics such as z or t. In both the proportion and mean inference contexts, we discuss the benefits of the proposed approaches and provide detailed examples that demonstrate the methods using the Rguroo statistical software.