Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 4: 80 (page 258)

Comparing weight-loss treatments Twenty overweight females have agreed to participate in a study of the effectiveness of four weight-loss treatments: A, B, C, and D. The researcher first calculates how overweight each subject is by comparing the subject’s actual weight with her “ideal” weight. The subjects and their excess weights in pounds are as follows:

The response variable is the weight lost after 8 weeks of treatment. Previous studies have shown that the effects of a diet may vary based on a subject’s initial weight.

(a) Explain why a randomized block design would be better than a completely randomized design in this setting.

(b) Should researchers form blocks of size 4 based on subjects’ last names in alphabetical order or by how overweight the subjects are? Explain.

(c) Use technology or Table D to carry out the random assignment required by your design. Explain your method clearly.

Short Answer

Expert verified

Part (a) Existence of blocks provides randomization in each block.

Part (b) Construct a block design based on overweight diet treatments.

Part (c) Construct four blocks based on excess weight that is, in the interval 0-20, 21-30, 31-40, 41-50.

Step by step solution

01

Part (a) Step 1. Explanation

Twenty overweight females participated in an experiment related to the effectiveness of four weight-loss treatments, that is, A, B, C, and D. These four weight-loss treatments are the block respective to which the effects of treatments are observed. As a result, there does not exist randomness in assigning treatment without any block. So, a completely randomized design is not applicable. In fact, the research design is randomized to each block which is why the research design is called randomized block design.

02

Part (b) Step 1. The basis of the construction of the block 

The blocks should be formed in order of the subject’s overweight and classify them into four overweight diet treatments.

03

Part (c) Step 1. Divide the dataset into four blocks or intervals. 

Consider 20 females data given, construct four blocks consisting of excess weight in the interval 0-20, 21-30, 31-40, 41-50. The randomized block design can be applied and random assignment of the treatment can be made among the block.

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

Comparing cancer treatments The progress of a type of cancer differs in women and men. Researchers want to design an experiment to compare three therapies for this cancer. They recruit 500male and 300female patients who are willing to serve as subjects.

(a) Which are the blocks in this experiment: the cancer therapies or the two sexes? Why?

(b) What are the advantages of a randomized block design over a completely randomized design using these 800subjects?

(c) Suppose the researchers had 800male and no female subjects available for the study. What advantage would this offer? What disadvantage?

Do placebos really work? Researchers in Japan conducted an experiment on 131 individuals who were extremely allergic to poison ivy. On one arm, each subject was rubbed with a poison ivy leaf and told the leaf was harmless. On the other arm, each subject was rubbed with a harmless leaf and told it was poison ivy. All the subjects developed a rash on the arm where the harmless leaf was rubbed. Of the

13subjects, 11 did not have any reaction to the real poison ivy leaf.

(a) What was the placebo in this experiment?

(b) Explain how the results of this study support the idea of a placebo effect.

Systematic random sample Sample surveys often use a systematic random sample to choose a sample of apartments in a large building or housing units in a block at the last stage of a multistage sample. Here is a description of how to choose a systematic random sample. Suppose that we must choose 4 addresses out of 100 Because 100/4=25 we can think of the list as four lists of 25 addresses. Choose 1 of the first 25 addresses at random using Table D. The sample contains this address and the addresses 25,50, and 75 places down the list from it. If the table gives 13, for example, then the systematic random sample consists of the addresses numbered 13,38,63, and 88

(a) Use Table D to choose a systematic random sample of 5 addresses from a list of 200 Enter the table at line 120

(b) Like an SRS, a systematic random sample gives all individuals the same chance to be chosen. Explain why this is true. Then explain carefully why a systematic sample is not an SRS.

Close shave Which of two brands of electric razor shaves closer? Describe how you would design and carry out an experiment to answer this question using

50adult male volunteers.

Room temperature and dexterity An expert on worker performance is interested in the effect of room temperature on the performance of tasks requiring manual dexterity. She chooses temperatures of 70°Fand 90°Fas treatments. The response variable is the number of correct insertions, during a 30-minute period, in a peg-and-hole apparatus that requires the use of both hands simultaneously. Each

subject is trained on the apparatus and then asked to make as many insertions as possible in 30 minutes of continuous effort.

(a) Outline a completely randomized design to compare dexterity at70° and 90°. Twenty subjects are available.

(b) Because individuals differ greatly in dexterity, the wide variation in individual scores may hide the systematic effect of temperature unless there are many subjects in each group. Describe in detail the design of a matched pairs experiment in which
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Calculus

Read Explanation

Logic and Functions

Read Explanation

Pure Maths

Read Explanation

Probability and Statistics

Read Explanation

Mechanics Maths

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