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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鈥檚 actual weight with her 鈥渋deal鈥� 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鈥檚 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鈥� 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鈥檚 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.

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Most popular questions from this chapter

How was your stay? A hotel has 30 floors with 40 rooms per floor. The rooms on one side of the hotel face the water, while rooms on the other side face a

golf course. There is an extra charge for the rooms with a water view. The hotel manager wants to survey 120 guests who stayed at the hotel during a convention about their overall satisfaction with the property.

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(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.

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(a) Explain how you would use technology or Table D to choose an SRS of 141 plots. Your description should be clear enough for a classmate to obtain your results.

(b) Use your method from (a) to choose the first 3 plots.
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