The Bowl of Wax Fruit

Master Stem was inspecting Student Leaf's work. Master Stem asked, "What is this calculation here?"

Student Leaf replied, "It is a confidence interval, Master Stem."

"And what is your confidence level?"

"It is a 95% confidence interval."

"So what does the 95% represent, Student Leaf? Is it a probability?"

"No, Master Stem, not for this particular interval. The 95% means that the random interval represented by this formula has a 95% probability of containing the unknown constant mu. But when I place numbers into the formula, the interval is no longer random. So I cannot say anything about the probability after I compute the interval."

"Do you remember the last time you visited my house? I had a bowl of wax fruit sitting on the table."

"Yes I remember, Master Stem. You removed the wax fruit from the table and placed real fruit on the table for our meal."

"This confidence interval of yours is like that wax fruit. It serves a purpose until you collect the data, then it becomes useless."

Creative Commons License This work is licensed under a Creative Commons Attribution 3.0 United States License. It was written by Steve Simon and was last modified on 2017-06-15. Category: Teaching resources