Let X₁,..., Xn be a random sample from a n(6,0²) population. Consider testing Ho: 01 ≤0 ≤ 02 versus H₁:0 <01 or 0 > 0₂. (a) Show that the test reject Ho if X>02+t-1.a/2√√/S2/n or X <01-tn-1.a/2√/S²/n is not a size a test. (b) Show that, for an appropriately chosen constant k, a size a test is given by reject Ho if X-|> k√√/S²/n,
Let X₁,..., Xn be a random sample from a n(6,0²) population. Consider testing Ho: 01 ≤0 ≤ 02 versus H₁:0 <01 or 0 > 0₂. (a) Show that the test reject Ho if X>02+t-1.a/2√√/S2/n or X <01-tn-1.a/2√/S²/n is not a size a test. (b) Show that, for an appropriately chosen constant k, a size a test is given by reject Ho if X-|> k√√/S²/n,
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text:Let X₁,..., Xn be a random sample from a n(0, 2) population. Consider testing
Ho: 01 ≤0 ≤ 02
versus H₁: 0 < 01 or 0 > 02.
(a) Show that the test
reject Ho if X > 02 + In-1₁a/2 √√/S²/n or X < 01 -tn-1₁a/2 √√/S²/n
is not a size a test.
(b) Show that, for an appropriately chosen constant k, a size a test is given by
reject Ho if X-> k√√/S²/n,
where 0 = (01 + 02)/2.
(c) Show that the tests in parts (a) and (b) are unbiased of their size. (Assume that
the noncentral t distribution has an MLR.)
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