In an experiment with t = 4 population means and sample sizes of n1 = 5, n2 = 6, n3 = 4, and n4= 8, consider the four linear combinations of the sample means:?̂1 = ?̅1 + 3?̅2 + ?̅3 + ?̅4?̂2 = ?̅1 + ?̅2 − 2?̅4?̂3 = ?̅1 + ?̅2 + ?̅3 + ?̅4?̂4 = ?̅1 + ?̅2 − 3?̅3 + ?̅4a. Which of the four linear combinations are contrastsb. Which pairs of contrasts are orthogonal 1. In an experiment with t= 4 population means and sample sizes of ni = 5, n2 = 6, n3 = 4, and n4= 8, consider the four linear combinations of the sample means:î = ỹ1 + 3ỹ2 + y3 + J41 = 9, + 92 – 2741z = y1 + J2 + ỹ3 + J4Î4 = 91 + Y2 – 393 + 94a. Which of the four linear combinations are contrastsb. Which pairs of contrasts are orthogonal

a. Consider the given four linear combinations of the sample means,…

Answered: 1. In an experiment with t = 4…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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In an experiment with t = 4 population means and sample sizes of n1 = 5, n2 = 6, n3 = 4, and n4= 8, consider the four linear combinations of the sample means:

?̂1 = ?̅1 + 3?̅2 + ?̅3 + ?̅4
?̂2 = ?̅1 + ?̅2 − 2?̅4
?̂3 = ?̅1 + ?̅2 + ?̅3 + ?̅4
?̂4 = ?̅1 + ?̅2 − 3?̅3 + ?̅4

a. Which of the four linear combinations are contrasts
b. Which pairs of contrasts are orthogonal

1. In an experiment with t= 4 population means and sample sizes of ni = 5, n2 = 6, n3 = 4, and n4
= 8, consider the four linear combinations of the sample means:
î = ỹ1 + 3ỹ2 + y3 + J4
1 = 9, + 92 – 274
1z = y1 + J2 + ỹ3 + J4
Î4 = 91 + Y2 – 393 + 94
a. Which of the four linear combinations are contrasts
b. Which pairs of contrasts are orthogonal

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