I developed the teaching materials for the purpose of a student learning such as the meaning of confidence interval, and the difference between standard deviation of a sample and the standard error of the mean, and so on, by analyzing numerical data by his own hand.
By performing data analysis by the Excel, it is shown that a set of pseudo random numbers (the sample-1, n = 10
6) generated by the programming source code (1), which is written in "Decimal BASIC", could be regarded as equal to a sample which is sampling from the population with the standard normal distribution. Therefore it turns out to be possible to treat the random numbers generated by the source code (1) as hypothetical measurements including errors obeying the axioms of error.
At first, a set of random numbers (sample-3, n=500) is generated by the source code (1), and then, copied onto the Excel sheet, in the teaching materials. A learner makes scatter diagrams, box-and-whisker plots, and histograms based on these data, and visually recognizes the distribution of the random numbers. Fitting Gaussian line to the histogram will aid in geometrical understanding of the meaning of the statistics such as mean and the standard deviation of the sample. Finally, 30 samples of n = 25 are generated, and analyzed. Comparing the basic statistic of each samples shows that there is possibility of the true value (the mean of the population) being not included in the range of 95 % confidence interval of the mean of the samples.
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