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Prove the 2-tailed case of the One-Sample t-test, i.e., if X₁, X2,..., Xn is a random sample from a normal distribution with mean and unknown variance o2, then define 71 T= χ-μο S/√n with S2 (X-X). Hence for the test of hypothesis Ho: μ = po n-1 i=1 versus H₁ μμo, at the level of significance o, reject Ho iff either t ≤-ta/2(n-1) or t≥ ta/2(n-1).

Prove the 2-tailed case of the One-Sample t-test, i.e., if X₁, X2,..., Xn is a random sample from a normal distribution with mean and unknown variance o2, then define 71 T= χ-μο S/√n with S2 (X-X). Hence for the test of hypothesis Ho: μ = po n-1 i=1 versus H₁ μμo, at the level of significance o, reject Ho iff either t ≤-ta/2(n-1) or t≥ ta/2(n-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
Section13.3: Special Probability Density Functions
Problem 30E
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Prove the 2-tailed case of the One-Sample t-test, i.e., if X₁, X2,..., Xn is a random sample from a normal distribution with mean and unknown variance o2, then define 71 1 X-μo T = S/√n with S2 (X-X)². Hence for the test of hypothesis Ho: μ = μo n-1 i=1 versus H₁ : μμo, at the level of significance a, reject Ho iff either t ≤-ta/2(n − 1) or t≥ ta/2(n-1).
Transcribed Image Text:Prove the 2-tailed case of the One-Sample t-test, i.e., if X₁, X2,..., Xn is a random sample from a normal distribution with mean and unknown variance o2, then define 71 1 X-μo T = S/√n with S2 (X-X)². Hence for the test of hypothesis Ho: μ = μo n-1 i=1 versus H₁ : μμo, at the level of significance a, reject Ho iff either t ≤-ta/2(n − 1) or t≥ ta/2(n-1).
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