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A materials scientist is experimenting with a new material

Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi ISBN: 9780073401331 38

Solution for problem 12SE Chapter 7

Statistics for Engineers and Scientists | 4th Edition

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Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi

Statistics for Engineers and Scientists | 4th Edition

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Problem 12SE

Problem 12SE

A materials scientist is experimenting with a new material with which to make beverage cans. She fills cans with liquid at room temperature, and then refrigerates them to see how fast they cool. According to Newton's law of cooling, if t is the time refrigerated and y is the temperature drop at time t. then y is related to t by an equation of the form

where β0 is a constant that depends on the initial temperature of the can and the ambient temperature of the refrigerator, and β1 is a constant that depends on the physical properties of the can. The scientist measures the temperature at regular intervals, and then fits this model to the data. The results are shown in the following figure. A scatterplot, with the least-squares line superimposed, is on the left, and the residual plot is on the right.

What should the scientist do next?

i. Try to find a transformation that makes the relationship more linear.

ii. Use the model as is, because Newton's law of cooling is a physical law.

iii. Use the model as is, because it fits well enough.

iv. Carefully examine the experimental setup to see what might have gone wrong.

Step-by-Step Solution:
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Chapter 7, Problem 12SE is Solved
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Textbook: Statistics for Engineers and Scientists
Edition: 4
Author: William Navidi
ISBN: 9780073401331

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A materials scientist is experimenting with a new material