Mathematical Statistics with Applications
7th Edition
ISBN: 9780495110811
Author: Dennis Wackerly, William Mendenhall, Richard L. Scheaffer
Publisher: Cengage Learning
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Textbook Question
Chapter 10.10, Problem 90E
Refer to Exercise 10.5.
a Find the power of test 2 for each of the following alternatives: θ = .1, θ = .4, θ = .7, and θ = 1.
b Sketch a graph of the power
c Compare the power function in part (b) with the power function that you found in Exercise 10.89 (this is the power function for test 1, Exercise 10.5). What can you conclude about the power of test 2 compared to the power of test 1 for all θ ≥ 0?
10.89 Refer to Exercise 10.5. Find the power of test 1 for each alternative in (a)–(e).
a θ = .1.
b θ = .4.
c θ = .7.
d θ = 1.
e Sketch a graph of the power function.
10.5 Let Y1 and Y2 be independent and identically distributed with a uniform distribution over the interval (θ, θ + 1). For testing H0: θ = 0 versus Ha: θ > 0, we have two competing tests:
Test 1: Reject H0 if Y1 > .95.
Test 2: Reject H0 if Y1 + Y2 > c.
Find the value of c so that test 2 has the same value for α as test 1. [Hint: In Example 6.3, we derived the density and distribution function of the sum of two independent random variables that are uniformly distributed on the interval (0, 1).]
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Pam, Rob and Sam get a cake that is one-third chocolate, one-third vanilla, and one-third strawberry as shown below. They wish to fairly divide the cake using the lone chooser method. Pam likes strawberry twice as much as chocolate or vanilla. Rob only likes chocolate. Sam, the chooser, likes vanilla and strawberry twice as much as chocolate. In the first division, Pam cuts the strawberry piece off and lets Rob choose his favorite piece. Based on that, Rob chooses the chocolate and vanilla parts. Note: All cuts made to the cake shown below are vertical.Which is a second division that Rob would make of his share of the cake?
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Chapter 10 Solutions
Mathematical Statistics with Applications
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