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# b.lect27 - Outline Tests Based on the t-Distribution...

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Outline Tests Based on the t -Distribution P -Values Precision in Hypothesis Testing Lecture 27 Chapter 9: Testing of Hypotheses Michael Akritas Michael Akritas Lecture 27 Chapter 9: Testing of Hypotheses

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Outline Tests Based on the t -Distribution P -Values Precision in Hypothesis Testing Tests Based on the t -Distribution Tests for the mean of a normal population Tests about the Regression Slope Tests about the Regression Line P -Values P -value for a Z -test P -value for a T -test Precision in Hypothesis Testing Calculation of β ( μ a ) Formulas for sample size determination Minitab Implementation Michael Akritas Lecture 27 Chapter 9: Testing of Hypotheses
Outline Tests Based on the t -Distribution P -Values Precision in Hypothesis Testing Tests for the mean of a normal population Tests about the Regression Slope Tests about the Regression Line General Formulation Michael Akritas Lecture 27 Chapter 9: Testing of Hypotheses

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Outline Tests Based on the t -Distribution P -Values Precision in Hypothesis Testing Tests for the mean of a normal population Tests about the Regression Slope Tests about the Regression Line General Formulation As mentioned before, an estimator θ of θ often satisfies, for all n , θ - θ σ ˆ θ t ν , with σ ˆ θ the estimated s.e. when sampling from normal populations. Michael Akritas Lecture 27 Chapter 9: Testing of Hypotheses
Outline Tests Based on the t -Distribution P -Values Precision in Hypothesis Testing Tests for the mean of a normal population Tests about the Regression Slope Tests about the Regression Line General Formulation As mentioned before, an estimator θ of θ often satisfies, for all n , θ - θ σ ˆ θ t ν , with σ ˆ θ the estimated s.e. when sampling from normal populations. In such cases, the TS for testing H 0 : θ = θ 0 is T H 0 = θ - θ 0 σ ˆ θ t ν , provided H 0 holds , Michael Akritas Lecture 27 Chapter 9: Testing of Hypotheses

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Outline Tests Based on the t -Distribution P -Values Precision in Hypothesis Testing Tests for the mean of a normal population Tests about the Regression Slope Tests about the Regression Line General Formulation As mentioned before, an estimator θ of θ often satisfies, for all n , θ - θ σ ˆ θ t ν , with σ ˆ θ the estimated s.e. when sampling from normal populations. In such cases, the TS for testing H 0 : θ = θ 0 is T H 0 = θ - θ 0 σ ˆ θ t ν , provided H 0 holds , and the RRs are: H a RR at level α θ > θ 0 T H 0 > t α,ν θ < θ 0 T H 0 < - t α,ν θ = θ 0 | T H 0 | > t α/ 2 Michael Akritas Lecture 27 Chapter 9: Testing of Hypotheses
Outline Tests Based on the t -Distribution P -Values Precision in Hypothesis Testing Tests for the mean of a normal population Tests about the Regression Slope Tests about the Regression Line General Formulation As mentioned before, an estimator θ of θ often satisfies, for all n , θ - θ σ ˆ θ t ν , with σ ˆ θ the estimated s.e. when sampling from normal populations. In such cases, the TS for testing H 0 : θ = θ 0 is T H 0 = θ - θ 0 σ ˆ θ t ν , provided H 0 holds , and the RRs are: H a RR at level α θ > θ 0 T H 0 > t α,ν θ < θ 0 T H 0

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