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Exercise 14. Let X₁, X2, X3 be independent Bernoulli trials, i.e. the X, are i.i.d. random variables with P(X₂ = 1) = p and P(X₂ = 0) = 1-p. We want to make inference about p, from observations 1, 2, 3 € {0, 1}. Assume we already know that either p = 0.3 or p = 0.8, and other values of p are not possible. In this case we want to decide whether the hypothesis Ho: p = 0.3 or the alternative H₁: p = 0.8 is more likely. Consider the test which rejects Ho if and only if s = => 2. For this test, determine the probabilities of type I and type II errors. 3

Exercise 14. Let X₁, X2, X3 be independent Bernoulli trials, i.e. the X, are i.i.d. random variables with P(X₂ = 1) = p and P(X₂ = 0) = 1-p. We want to make inference about p, from observations 1, 2, 3 € {0, 1}. Assume we already know that either p = 0.3 or p = 0.8, and other values of p are not possible. In this case we want to decide whether the hypothesis Ho: p = 0.3 or the alternative H₁: p = 0.8 is more likely. Consider the test which rejects Ho if and only if s = => 2. For this test, determine the probabilities of type I and type II errors. 3

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 29E
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Exercise 14. Let X₁, X2, X3 be independent Bernoulli trials, i.e. the X; are i.i.d. random variables with P(X₂ = 1) = p and P(X; = 0) = 1-p. We want to make inference about p, from observations x1, x2, x3 = {0, 1}. - Assume we already know that either p = 0.3 or p = 0.8, and other values of p are not possible. In this case we want to decide whether the hypothesis Ho: p = 0.3 or the alternative H₁: p = 0.8 is more likely. Consider the test which rejects Ho if and only if s := ³-₁ ; ≥ 2. For this test, determine the probabilities of type I and type II errors.
Transcribed Image Text:Exercise 14. Let X₁, X2, X3 be independent Bernoulli trials, i.e. the X; are i.i.d. random variables with P(X₂ = 1) = p and P(X; = 0) = 1-p. We want to make inference about p, from observations x1, x2, x3 = {0, 1}. - Assume we already know that either p = 0.3 or p = 0.8, and other values of p are not possible. In this case we want to decide whether the hypothesis Ho: p = 0.3 or the alternative H₁: p = 0.8 is more likely. Consider the test which rejects Ho if and only if s := ³-₁ ; ≥ 2. For this test, determine the probabilities of type I and type II errors.
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