An Introduction to Mathematical Statistics and Its Applications (6th Edition)
An Introduction to Mathematical Statistics and Its Applications (6th Edition)
6th Edition
ISBN: 9780134114217
Author: Richard J. Larsen, Morris L. Marx
Publisher: PEARSON
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Chapter 12.4, Problem 1Q

The cathode warm-up time (in seconds) was determined for three different types of X-ray tubes using fifteen observations of each type. The results are listed in the following table.

Warm-Up Times (sec)
Tube Type
ABC
19 27 20 24 16 14
23 31 20 25 26 18
26 25 32 29 15 19
18 22 27 31 18 21
20 23 40 24 19 17
18 29 22 32 19 18
35 18 18

Do an analysis of variance on these data and test the hypothesis that the three tube types require the same average warm-up time. Include a pair of orthogonal contrasts in your ANOVA table. Define one of the contrasts so it tests H 0 : μ A = μ C . What does the other contrast test? Check to see that the sums of squares associated with your two contrasts verify the statement of Theorem 12.4.1.

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