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Chapter 2: Problem 69

A manufacturer of clay roofing tiles would like to investigate the effect of clay type on the proportion of tiles that crack in the kiln during firing. Two different types of clay are to be considered. One hundred tiles can be placed in the kiln at any one time. Firing temperature varies slightly at different locations in the kiln, and firing temperature may also affect cracking. Discuss the design of an experiment to collect information that could be used to decide between the two clay types. How does your proposed design deal with the extraneous factor temperature?

Short Answer

Expert verified
An appropriate experimental design would involve dividing the 100 tiles equally among the two types of clay, distributing them randomly in the kiln to account for variation in temperature, and then comparing the proportion of tiles that crack for each type of clay. Dealing with the 'extraneous' temperature factor can be achieved by randomly distributing tiles of each clay type throughout the kiln.

Step by step solution

01

Define the Experiment

Since the objective is to observe the effect of two types of clay on the proportion of tiles that crack in the kiln, an appropriate design would be to randomly partition the 100 tiles to be fired into two groups of 50. Each group would be made from one type of clay.
02

Address the Confounding Variable

To account for the varying temperatures in different parts of the kiln, ensure that tiles for each type of clay are randomly placed throughout the kiln. This would help to average out any effects the different kiln temperatures might have on the two types of clay.
03

Collect and Analyze Data

After firing, collect data on the proportion of tiles that cracked for each clay type. Compare these proportions to decide which clay type has a lesser tendency to crack in the kiln. This comparison can be made using a proportion comparison statistical test.
04

Address the Solution

Discuss how this design deals with the variable of temperature: By distributing the tiles made from each kind of clay randomly throughout the kiln, this design helps to account for the effect of different temperatures within the kiln on the proportion of tiles that crack.\

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