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Chapter 1: Q 1.93. (page 30)

In Exercises 1.92-1.97, we present descriptions of designed experiments. In each case, identify the

(a) experimental units

(b) response variable

(c) factor (s)

(d) levels of each factor:-

(e) treatments.

Highway Signs. A driver's ability to detect highway signs is an important consideration in highway safety. In his dissertation, High way Construction Safety and the Aging Driver, S. Younes investigated the distance at which drivers can first detect highway caution signs. This distance is called the detection distance. Younes analyzed the effect that sign size and sign material have on detection distance. Drivers were randomly assigned to one combination of sign size ( small, medium, and large ), and sign material ( 1, 2, and 3 ). Each driver covered the same stretch of highway at a constant speed during the same time of day, and the detection distance, in feet, was determined for the driver's assigned caution sign.

Short Answer

Expert verified

(a) experimental units:- Drivers

(b) response variable:- Detection distance.

(c) factor (s):- sign size and sign material.

(d) levels of each factor:-

sign size includes small, medium, and large.

and sign material includes 1, 2, and 3.

(e) treatments:- Nine.

Step by step solution

01

Part (a) Step 1. Given information.

The given statement is:

A driver's ability to detect highway signs is an important consideration in highway safety. In his dissertation,High way Construction Safety and the Aging Driver, S. Younes investigated the distance at which drivers can first detect highway caution signs. This distance is called thedetection distance. Younes analyzed the effect that sign size and sign material have on detection distance. Drivers were randomly assigned to one combination of sign size ( small, medium, and large ), and sign material ( 1, 2, and 3 ). Each driver covered the same stretch of highway at a constant speed during the same time of day, and the detection distance, in feet, was determined for the driver's assigned caution sign.

02

Part (a) Step 2. Identify the experimental units.

Taking into consideration the given designed experiment, Experimental units are the drivers that are being studied in this study.

03

Part (b) Step 1. Identify the response variable.

The response variable, of the given designed experiment, is the detection distance.

Because the researcher investigated the distance at which drivers can first detect highway caution signs. This distance is called the detection distance.

04

Part (c) Step 1. Identify the factor.

Here, the factors include: sign size and sign material.

Because researchers analyzed the effect that sign size and sign material have on detection distance.

05

Part (d) Step 1. Identify the levels of each factor.

The three levels of sign size include:

  1. small
  2. Medium
  3. Large

The three levels of sign material include:

1, 2 and 3.

06

Part (e) Step 1. Identify the treatments.

It includes the nine different possible ways of three levels of sign size and three levels of sign material.

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Most popular questions from this chapter

In a designed experiment, there are two factors, say, Factor Aand Factor B. Factor Ahas three levels, say, a1,a2anda3; Factor Bhas four levels, say,b1,b2,b3andb4.

(a) Construct a schematic for the treatments similar to Table 1.8 on page 27.

(b) Use part ( a ) to determine the number of treatments.

(c) Could you have determined the answer for part ( b ) without constructing the schematic in part ( a )? Explain your answer.

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(b) Which method is easier: simple random sampling or systematic random sampling?

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Wasp Hierarchical Status. In an issue of Discover (Vol. 26, No. 2, pp. 10-11), J. Netting described the research of E. Tibbetts of the University of Arizona in the article, "The Kind of Face Only a Wasp Could Trust." Tibbetts found that wasps signal their strength and status with the number of black splotches on their yellow faces, with more splotches denoting higher status. Tibbetts decided to see if she could cheat the system. She painted some of the insects ' faces to make their status appear higher or lower than it really was. She then placed the painted wasps with a group of female wasps to see if painting the faces altered their hierarchical status. Was this investigation an observational study or a designed experiment? Justify your answer.

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