Let X1, . . . , Xn be a random sample from a pdf that is symmetric about . An estimator...

Let X₁, . . . , X_n be a random sample from a pdf that is symmetric about . An estimator for that has been found to perform well for a variety of underlying distributions is the Hodges–Lehmann estimator. To define it, first compute for

Compute the value of this estimate using the data of Exercise 44 of Chapter 1. [Hint: Construct a square table with the x_i’s listed on the left margin and on top. Then compute averages on and above the diagonal.]

Reference exercise 44 in chapter 1

The article “Oxygen Consumption During Fire Suppression: Error of Heart Rate Estimation” (Ergonomics, 1991: 1469–1474) reported the following data on oxygen consumption (mL/kg/min) for a sample of ten firefighters performing a fire-suppression simulation:

Compute the following:

a. The sample range

b. The sample variance s² from the definition (i.e., by first computing deviations, then squaring them, etc.)

c. The sample standard deviation

d. s² using the shortcut method