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9. Let X₁,..., X10 denote a random sample of size 10 of a Poisson distribution with mean 0. Show that the test that rejects H₁ : 0 = 0.1 in favour of H₁ : 0 = 0.5 if Σ1₁ X; ≥ 3 is most powerful. Determine, for this test, the significance level a and the power at 0 = 0.5.

9. Let X₁,..., X10 denote a random sample of size 10 of a Poisson distribution with mean 0. Show that the test that rejects H₁ : 0 = 0.1 in favour of H₁ : 0 = 0.5 if Σ1₁ X; ≥ 3 is most powerful. Determine, for this test, the significance level a and the power at 0 = 0.5.

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
Section13.2: Expected Value And Variance Of Continuous Random Variables
Problem 10E
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9. Let X₁,..., X₁0 denote a random sample of size 10 of a Poisson distribution with mean 0. Show that the test that rejects H₁ : 0 = 0.1 in favour of H₁ : 0 = 0.5 if ΣX; ≥ 3 is most powerful. Determine, for this test, the significance level a and the power at 0 = 0.5.
Transcribed Image Text:9. Let X₁,..., X₁0 denote a random sample of size 10 of a Poisson distribution with mean 0. Show that the test that rejects H₁ : 0 = 0.1 in favour of H₁ : 0 = 0.5 if ΣX; ≥ 3 is most powerful. Determine, for this test, the significance level a and the power at 0 = 0.5.
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