10. Consider a random sample from some distribution that depends on the parameter 0 > 0. The hypotheses of interest are Ho: 0 <00 vs H₁: 0>00 for 00 = 2. We will consiser the test with rejection region R = {T < c}, where T = T(X) is the appropriate test statistic. The test statistic T is known to have the following PDF: Ө fo(t) = to+1' t> 1. (a) Find the power function for this test (as a function of 0 and c). (b) Find the value of c such that this test will be size a for 80 = 2. (c) Find the probability of a Type II error at 0 = 4. (d) If = 1, what is the probability of making an error? Is it Type I or Type II? (e) Assuming a = 0.10, what is the decision if the observed data provides t = 1.2?
10. Consider a random sample from some distribution that depends on the parameter 0 > 0. The hypotheses of interest are Ho: 0 <00 vs H₁: 0>00 for 00 = 2. We will consiser the test with rejection region R = {T < c}, where T = T(X) is the appropriate test statistic. The test statistic T is known to have the following PDF: Ө fo(t) = to+1' t> 1. (a) Find the power function for this test (as a function of 0 and c). (b) Find the value of c such that this test will be size a for 80 = 2. (c) Find the probability of a Type II error at 0 = 4. (d) If = 1, what is the probability of making an error? Is it Type I or Type II? (e) Assuming a = 0.10, what is the decision if the observed data provides t = 1.2?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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The questions that I need help with are 10(d) and (e). Thank you.
Transcribed Image Text:10. Consider a random sample from some distribution that depends on the parameter > 0. The
hypotheses of interest are Ho000 vs H₁: 0>00 for 00 = 2. We will consiser the test with
rejection region R = {T < c}, where T = T(X) is the appropriate test statistic. The test statistic
T is known to have the following PDF:
0
fo(t) =
=
to+1'
t > 1.
(a) Find the power function for this test (as a function of 0 and c).
(b) Find the value of c such that this test will be size a for 80 = 2.
(c) Find the probability of a Type II error at 0 = 4.
(d) If 0 = 1, what is the probability of making an error? Is it Type I or Type II?
(e) Assuming a = 0.10, what is the decision if the observed data provides t = 1.2?
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VIEWStep 2: Compute the power function for this test.
VIEWStep 3: Compute the value of c such that this test will be size α for θ_0 = 2.
VIEWStep 4: Compute the probability of type II error at θ = 4.
VIEWStep 5: Compute the probability of making an error.
VIEWStep 6: Determine the decision if observed data provides t = 1.2.
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