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a) Let Y be a random variable whose probability density function and cumulative distribution function is given by and, f(y; 0) = ey-0 (1+ey-8)² F(y; 0) = 1- 1+ey-0 -∞ 1. ii) Find the power of the test which rejects Ho if Y > 1. iii) If a test that rejects Ho given Y₁ ≥c is considered. What will be the value of c when the level of significance of the test is 0.1.

a) Let Y be a random variable whose probability density function and cumulative distribution function is given by and, f(y; 0) = ey-0 (1+ey-8)² F(y; 0) = 1- 1+ey-0 -∞ 1. ii) Find the power of the test which rejects Ho if Y > 1. iii) If a test that rejects Ho given Y₁ ≥c is considered. What will be the value of c when the level of significance of the test is 0.1.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.CR: Chapter 13 Review
Problem 3CR
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a) Let Y be a random variable whose probability density function and cumulative distribution function is given by and, f(y; 0) = QUESTION 4 ey-0 (1+ey-8)2, F(y; 0) = 1 - 1 1+ey-0 -∞ <y<∞ and -∞o < 0 < 0, -∞0⁰ <y <∞ and -∞o < 0 <∞, respectively. Suppose that it is desired to test the null hypothesis Ho: 0 = 0 against the alternative hypothesis H₁:0 = 1 using one random observation Y. i) Find the level of significance which rejects Ho if Y > 1. ii) Find the power of the test which rejects Ho if Y > 1. iii) If a test that rejects Ho given Y₁ ≥c is considered. What will be the value of c when the level of significance of the test is 0.1.
Transcribed Image Text:a) Let Y be a random variable whose probability density function and cumulative distribution function is given by and, f(y; 0) = QUESTION 4 ey-0 (1+ey-8)2, F(y; 0) = 1 - 1 1+ey-0 -∞ <y<∞ and -∞o < 0 < 0, -∞0⁰ <y <∞ and -∞o < 0 <∞, respectively. Suppose that it is desired to test the null hypothesis Ho: 0 = 0 against the alternative hypothesis H₁:0 = 1 using one random observation Y. i) Find the level of significance which rejects Ho if Y > 1. ii) Find the power of the test which rejects Ho if Y > 1. iii) If a test that rejects Ho given Y₁ ≥c is considered. What will be the value of c when the level of significance of the test is 0.1.
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