Chapter 12, Problem 21SE

Swimsuits and Racing Speeds (Example 3) New, slick swimsuits were introduced in the 2008 summer Olympics, and some say that they gave the wearers an advantage in races. In order to test whether the suits were effective, suppose that there are 40 swimmers; 20 of them are Olympic-level swimmers, and 20 are amateur swimmers. The designers will ask the swimmers to swim 200 meters as fast as possible. It is reasonable to assume that the effects of the suits (due to dynamic forces of the water) might be different for the elite Olympic swimmers than for regular swimmers.

a. Identify the treatment variable and the response variable.

b. Describe a simple randomized design (not blocked) to test whether the slick suits decrease race times. Explain in detail how you will assign swimmers to treatment groups. Your description should be detailed enough that a friend could carry out your instructions.

c. Describe a blocked design to test whether the slick suits decrease race times. Explain in detail how you will assign swimmers to treatment groups.

d. What advantage does the blocked design have?

e. Describe a way to use swimmers as their own controls to reduce variation.