Step by step, the Wald score interval is constructed. Photo: Jean-Baptiste Béranger

In the article, "A Classroom Approach to the Construction of an Approximate Confidence Interval of a Poisson Mean Using One Observation" Per-Gösta Andersson explains confidence intervals in the form of a discussion with a student.

Step by step, it is shown how to construct the Wald score interval for a Poisson mean. According to Per-Gösta Andersson, the Wald score interval "exhibits better properties" but still is "not much more difficult to construct" than the approximate two-sided Wald confidence interval.

Students that have studied mathematical statistics for at least one semester should be able to follow the discussion in the article, which you can read it here.