Chapter 4.2, Problem 82E

(a)

To determine

To explain and identify the flaws you see in the proposed design for this experiment.

Explanation of Solution

In this study, the researchers wanted to study that which of the two brands A or brand B of electric razor shaves closer.

There are some flaws in the experiment that is confounding variable of left hand vs. right hand.The dominant hand of the man may have an effect on the closeness of the shave more so than the quality of the razor. Thus these flaws will affect the result of the study.

(b)

To determine

To describe how you would design the experiment and explain how your design addresses each of the problems you identified in part (a).

Explanation of Solution

In this study, the researchers wanted to study that which of the two brands A or brand B of electric razor shaves closer.

The design we will use is the matched pairs design but randomly determine which razor brand shaves which face side. That is,

  $\begin{array}{l}\text{Group 1: 25 men}\\ \text{Treatment 1: Razor brand X on left Razor brand Y on right }\\ \text{and rate shaving closeness on each side of face}\text{.}\\ \text{Group 2: 25 men}\\ \text{Treatment 2: Razor brand X on right Razor brand Y on left}\text{.}\end{array}$

Random Assignment Randomization: label the men $\text{1 to 50}$ . Using a random number generator, randomly generate $25$ different numbers between $1\text{ and }50$ , ignoring repeats. The men corresponding to these first $25$ selected number receive treatment $1$ , the rest of the men receive treatment $2$ .

We will use this design because this eliminates the confounding variable of dominant hand because both razors are being tested on both sides of the face.