Suppose 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 x

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x1, x2,

c, xn

(d/dy) f 21 x 5 f (y) 5 1/fr(x) 21

(y)

y 5 f(x)

za 5 21 z (1 2

a) a, (za) 5 1 2 a g 5 a/2 w 5 s(zg 1 za2g x# )/ 1n g 2 a/2 g 5 a/2 ax 2 zg # s 1n

, x 1 za2g # s 1n b 0 # g # a 100(1 2 a)

x x2 5 3.5, x3 5 1.7, x4 5 1.2 5 5 2.4 Understanding Robust and Exploratory Data Analysis

(see the bibliography in Chapter 6) suggests the following robust 95% CI for the population mean (point of symmetry):

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