Suppose x1, x2, ……, xn are observed values resulting from a random sample from a symmetr...

Suppose x₁, x₂, ……, x_n are observed values resulting from a random sample from a symmetric but possibly heavy-tailed distribution. Let and fs denote the sample median and fourth spread, respectively. Chapter 11 of

Understanding Robust and Exploratory Data Analysis (see the bibliography in Chapter 6) suggests the following robust 95% CI or the population mean (point of symmetry):

The value of the quantity in parentheses is 2.10 for n = 10 , 1.94 for n = 20 , and 1.91 for n = 30 . Compute this CI for the data of Exercise 45, and compare to the t CI appropriate for a normal population distribution.