통계적 추론에서의 표집분포 개념 지도를 위한 시뮬레이션 소프트웨어 설계 및 구현

The Design and Implementation to Teach Sampling Distributions with the Statistical Inferences

본 논문의 목적은 고등학교 수준의 학생들이 표집분포의 개념을 학습할 수 있도록 '표집분포 시뮬레이션 (Sampling Distributions Simulation)'을 설계하고 구현하는 것이다. '표집분포 시뮬레이션'은 다음과 같이 4차시로 구성되어 있다. 1차시-신뢰도와 신뢰구간의 의미 학습하기 2차시-표집분포의 의미 학습하기 3차시-중심극한정리의 의미 학습하기 4차시-이항분포의 정규근사 학습하기 본 연구를 통하여 표집분포의 중요성에 대한 학생들이 인식이 달라지고 이해가 증진되기를 기대한다. 또 본 연구의 결과로 제공되는 프로그램 '표집분포의 시뮬레이션' 수업을 통해 통계적 추론 능력이 향상되고, 아울러 통계적 추론 속에서 표집 분포의 역할이 충분히 이해되기를 기대한다.

The purpose of the study is designing and implementing 'Sampling Distributions Simulation' to help students to understand concepts of sampling distributions. This computer simulation is developed to help students understand sampling distributions more easily. 'Sampling Distributions Simulation' consists of 4 sessions. 'The first session - Confidence level and confidence intervals - includes checking if the intended confidence level is actually achieved by the real relative frequency for the obtained sample confidence intervals containing population mean. This will give the students clearer idea about confidence level and confidence intervals in addition to the role of sampling distribution of the sample means among those. 'The second session - Sampling Distributions - helps understand sampling distribution of the sample means, through the simulation method to make comparison between the histogram of sampling distributions and that of the population. The third session - The Central Limit Theorem - includes calculating the means of the samples taken from a population which follows a uniform distribution or follows a Bernoulli distribution and then making the histograms of those means. This will provides comprehension of the central limit theorem, which mentions about the sampling distribution of the sample means when the sample size is very large. The forth session - the normal approximation to the binomial distribution - helps understand the normal approximation to the binomial distribution as an alternative version of central limit theorem. With the practical usage of the shareware 'Sampling Distributions Simulation', we expect students to have a new vision on the sampling distribution and to get more emphasis on it. With the sound understandings on the sampling distributions, more accurate and profound statistical inferences are expected. And the role of the sampling distribution in the inferences should be more deeply appreciated.