Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 1: Q 1.87. (page 29)

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.

Short Answer

Expert verified

Part (a)

Part (b) 12

Part (c) 12

Step by step solution

01

Part (a) Step 1. Given information.

The given statement is:

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.

02

Part (a) Step 2. Construct a schematic for the treatments similar to Table 1.8 on page 27.

Construct a schematic for the treatments as shown below:

03

Part (b) Step 1. Determine the number of treatments.

There are twelve combinations based on the schematic for the treatments obtained in part (a).

As a result, there are a total of twelve treatments.

04

Part (c) Step 1. Determine the number of treatments without constructing the schematic.

The number of levels for factor Ais three, while factor Bhas four levels.

The number of treatments will equal the product of factor Aand factor B:

=NumberoflevelsoffactorA×NumberoflevelsoffactorB=3×4=12

As a result, The total number of levels is 12.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

In a designed experiment, there are two factors, say, Factor Aand Factor B. Factor Ahas four levels, say, a1,a2,a3anda4; Factor B has two levels, say,b1andb2.

(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.

Fill in the following blank:

Observational studies can reveal only association, whereas experiments can help establish .

Identify some methods used in descriptive statistics.

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.

Increasing Unit Sales. Supermarkets are interested in strategies to increase temporarily the unit sales of a product. In one study, researchers compared the effect of display type and price on unit sales for a particular product. The following display types and pricing schemes were employed.

  • Display types: normal display space interior to an aisle, normal display space at the end of an aisle, and enlarged display space.
  • Pricing schemes: regular price, reduced price, and cost.

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.

Dexamethasone and IQ. In the paper "Outcomes at School Age After Postnatal Dexamethasone Therapy for Lung Disease of Prematurity" (New England Journal of Medicine,Vol . 350, No. 13, pp . 1304-1313), T. Yeh et al . studied the outcomes at school age in children who had participated in a double-blind, placebo-controlled trial of early postnatal dexamethasone therapy for the prevention of chronic lung disease of prematurity. One result reported in the study was that, at school age, the control group of 74 children had an average IQ score of 84.4, whereas the dexamethasone group of 72 children had an average IQ score of 78.
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Calculus

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Probability and Statistics

Read Explanation

Applied Mathematics

Read Explanation

Geometry

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free