/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 84 A manufacturer of clay roofing t... [FREE SOLUTION] | 91影视

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Chapter 2: Problem 84

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 variable temperature?

Short Answer

Expert verified
To conduct the experiment, make 50 tiles from each clay type and fire them together in the kiln after random placement. This allows for a fair comparison between the two clays, while the random placement ensures the effect of temperature variability in the kiln is evenly distributed between the two types of clay. After firing, the cracked tiles from each clay type are counted, and a statistical comparison of the proportions is performed to decide the more suitable clay.

Step by step solution

01

Identifying the Response Variable

The response variable is the proportion of tiles that crack during firing. This is what will be measured and compared across the two types of clay.
02

Handling Explanatory Variables

There are two types of clay being considered, making these the explanatory variables. One could create two groups of 50 tiles each, one group made from the first clay type and the other from the second type. These would then be fired together in the kiln.
03

Dealing with Potential Confounding Variable

To handle the temperature variable, since temperature varies in different locations in the kiln, it might be effective to mix the tiles of both types randomly in the kiln space. This way, the impact of the temperature would be approximately equally likely for tiles from both clay types, reducing bias.
04

Collection of Data and Conclusion

Once the tiles are fired, collect the data by noting the number of tiles of each clay type that have cracked. Then, perform a statistical analysis to compare the proportions of cracked tiles between the two clay types.

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