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For the following pairs of assertions, • Indicate which of these don't constitute a valid hypothesis test, and • Why they do (or don't) constitute a valid hypothesis test 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Ho : μχ = 100 Ho : x = 100 Ho: max(X₁, X2,..., Xn) = 100 Ho : ax = 20 US. VS. VS. VS. Ho: p = 0.25 Ho : μ.x – My = 25 Ho: ss Ho: μ = 120 Ho: ox/oy = 1 Ho px py=-0.1 VS. US. VS. vs. VS. VS. H@ : μχ < 100 Ha :ay <100 Ha max(X₁, X2,...,xn) < 100 Ha: ox ≤ 20 Ha: p = 0.25 H@ : μχ - My > 100 H₁ : 8² 83 Ha μ = 150 H„: σχ/σy #1 Ha: px -py <-0.1 Hint • Here X₁, X2,..., X, "N(μx, o) and Y₁, Y2,..., Ym are the sample variances • Alternatively, X₁, X2,..., X₂ Ber(px) and concerning p. tid N(μy, o). sx and sy Y₁, Y2,..., Ym id Ber(px) and Y₁, Y2,..., Ymd Ber(py) for the tes

For the following pairs of assertions, • Indicate which of these don't constitute a valid hypothesis test, and • Why they do (or don't) constitute a valid hypothesis test 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Ho : μχ = 100 Ho : x = 100 Ho: max(X₁, X2,..., Xn) = 100 Ho : ax = 20 US. VS. VS. VS. Ho: p = 0.25 Ho : μ.x – My = 25 Ho: ss Ho: μ = 120 Ho: ox/oy = 1 Ho px py=-0.1 VS. US. VS. vs. VS. VS. H@ : μχ < 100 Ha :ay <100 Ha max(X₁, X2,...,xn) < 100 Ha: ox ≤ 20 Ha: p = 0.25 H@ : μχ - My > 100 H₁ : 8² 83 Ha μ = 150 H„: σχ/σy #1 Ha: px -py <-0.1 Hint • Here X₁, X2,..., X, "N(μx, o) and Y₁, Y2,..., Ym are the sample variances • Alternatively, X₁, X2,..., X₂ Ber(px) and concerning p. tid N(μy, o). sx and sy Y₁, Y2,..., Ym id Ber(px) and Y₁, Y2,..., Ymd Ber(py) for the tes

MATLAB: An Introduction with Applications
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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For the following *pairs of assertions*, - Indicate which of these don't constitute a valid hypothesis test, and - Why they do (or don't) constitute a valid hypothesis test 1. \( H_0 : \mu_X = 100 \quad \text{vs.} \quad H_a : \mu_X < 100 \) 2. \( H_0 : \mu_X = 100 \quad \text{vs.} \quad H_a : \mu_Y < 100 \) 3. \( H_0 : \max(X_1, X_2, \ldots , X_n) = 100 \quad \text{vs.} \quad H_a : \max(X_1, X_2, \ldots , X_n) < 100 \) 4. \( H_0 : \sigma_X = 20 \quad \text{vs.} \quad H_a : \sigma_X \leq 20 \) 5. \( H_0 : p \neq 0.25 \quad \text{vs.} \quad H_a : p = 0.25 \) 6. \( H_0 : \mu_X - \mu_Y = 25 \quad \text{vs.} \quad H_a : \mu_X - \mu_Y > 100 \) 7. \( H_0 : s_X^2 = s_Y^2 \quad \text{vs.} \quad H_a : s_X^2 \neq s_Y^2 \) 8. \( H_0 : \mu = 120 \quad \text{vs.} \quad H_a : \mu = 150 \) 9. \( H_0 : \sigma_X / \sigma_Y = 1 \quad \text{vs.} \quad H_a : \sigma_X / \sigma_Y \neq 1 \) 10. \( H_0 : p_X - p_Y = -0.1 \quad \text{vs.} \quad H_a : p_X - p_Y < -0.1 \) **Hint** - Here \( X_1, X_2, \ldots, X_n \overset{\text{iid}}{\sim} N(\mu_X, \sigma_X^2) \) and \( Y_1, Y_2, \ldots, Y_m \
Transcribed Image Text:For the following *pairs of assertions*, - Indicate which of these don't constitute a valid hypothesis test, and - Why they do (or don't) constitute a valid hypothesis test 1. \( H_0 : \mu_X = 100 \quad \text{vs.} \quad H_a : \mu_X < 100 \) 2. \( H_0 : \mu_X = 100 \quad \text{vs.} \quad H_a : \mu_Y < 100 \) 3. \( H_0 : \max(X_1, X_2, \ldots , X_n) = 100 \quad \text{vs.} \quad H_a : \max(X_1, X_2, \ldots , X_n) < 100 \) 4. \( H_0 : \sigma_X = 20 \quad \text{vs.} \quad H_a : \sigma_X \leq 20 \) 5. \( H_0 : p \neq 0.25 \quad \text{vs.} \quad H_a : p = 0.25 \) 6. \( H_0 : \mu_X - \mu_Y = 25 \quad \text{vs.} \quad H_a : \mu_X - \mu_Y > 100 \) 7. \( H_0 : s_X^2 = s_Y^2 \quad \text{vs.} \quad H_a : s_X^2 \neq s_Y^2 \) 8. \( H_0 : \mu = 120 \quad \text{vs.} \quad H_a : \mu = 150 \) 9. \( H_0 : \sigma_X / \sigma_Y = 1 \quad \text{vs.} \quad H_a : \sigma_X / \sigma_Y \neq 1 \) 10. \( H_0 : p_X - p_Y = -0.1 \quad \text{vs.} \quad H_a : p_X - p_Y < -0.1 \) **Hint** - Here \( X_1, X_2, \ldots, X_n \overset{\text{iid}}{\sim} N(\mu_X, \sigma_X^2) \) and \( Y_1, Y_2, \ldots, Y_m \
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