| Research has found that students successfully complete an introductory course in statistics without fully comprehending the underlying theory or being able to exhibit statistical reasoning. This is particularly true for the understanding about the sampling distribution of the mean, a crucial concept for statistical inference.;This study investigates two different types of students, sensor and intuitor, based on a preferred style of learning, in how they answer questions about sampling distributions and how they demonstrate reasoning and logic regarding these answers. Ten sections of introductory statistics are taught at North Carolina State University over three semesters and data is collected from eight final exam questions. These final exam questions are analyzed using both quantitative and qualitative analysis techniques. Differences between the groups are summarized, if they exist. This study also explores foundational questions and their relationship to understanding the sampling distribution of the mean.;The analysis of data showed differences between the sensor and intuitor on three of the eight questions, but the level of significance is not very high. No evidence is found to support that if a student understands a series of questions thought to be foundational to understanding of sampling distributions then they should exhibit statistical reasoning. Although there was no evidence to show that there is a largely observable difference between the sensor and intuitor on all eight activities, there is evidence to support common misconceptions that students reason about a sampling distribution of means as though it were a simple random sample. Further research is needed to investigate the lexical ambiguity amongst key terms and definitions and how it affects the performance in the classroom as well as how students fail to make the connection between a simple random sample and a sampling distribution of the mean. |
