Per Gösta Andersson: A classroom approach to the construction of an approximate confidence interval of a Poisson mean using one observation

Even elementary statistical problems may give rise to a deeper and broader discussion of issues in probability and statistics. The construction of an approximate confidence interval for a Poisson mean turns out to be such a case. The “standard” two-sided Wald confidence interval is discussed and compared with the score interval. The analysis of this interval estimation problem involves topics such as asymptotic normality and the correspondence between tests and confidence regions. The discussion is partly in the form of an imaginary dialogue between a teacher and a student.