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Math 203_Lecture 12

# Math 203_Lecture 12 - Principles of Statistics 1 Lecture 12...

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Principles of Statistics 1 Lecture 12: Math 203 Abbas Khalili Department of Mathematics and Statistics McGill University May 19, 2011 Principles of Statistics 1 Lecture 12: Math 203 – p. 1/3

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Large sample one-sided hypothesis test Hypothesis test for the population mean μ : Principles of Statistics 1 Lecture 12: Math 203 – p. 2/3
Large sample one-sided hypothesis test Hypothesis test for the population mean μ : In general, if we have hypotheses of the form H 0 : μ μ 0 vs. H A : μ > μ 0 Principles of Statistics 1 Lecture 12: Math 203 – p. 2/3

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Large sample one-sided hypothesis test Hypothesis test for the population mean μ : In general, if we have hypotheses of the form H 0 : μ μ 0 vs. H A : μ > μ 0 then the test statistic is Z = ¯ X μ 0 s/ n Principles of Statistics 1 Lecture 12: Math 203 – p. 2/3
Large sample one-sided hypothesis test Hypothesis test for the population mean μ : In general, if we have hypotheses of the form H 0 : μ μ 0 vs. H A : μ > μ 0 then the test statistic is Z = ¯ X μ 0 s/ n and we reject H 0 if Z > z α . The type I error will be no larger than α . Principles of Statistics 1 Lecture 12: Math 203 – p. 2/3

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Large sample one-sided hypothesis test Hypothesis test for the population mean μ : Principles of Statistics 1 Lecture 12: Math 203 – p. 3/3
Large sample one-sided hypothesis test Hypothesis test for the population mean μ : In general, if we have hypotheses of the form H 0 : μ μ 0 vs. H A : μ < μ 0 Principles of Statistics 1 Lecture 12: Math 203 – p. 3/3

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Large sample one-sided hypothesis test Hypothesis test for the population mean μ : In general, if we have hypotheses of the form H 0 : μ μ 0 vs. H A : μ < μ 0 then the test statistic is Z = ¯ X μ 0 s/ n Principles of Statistics 1 Lecture 12: Math 203 – p. 3/3
Large sample one-sided hypothesis test Hypothesis test for the population mean μ : In general, if we have hypotheses of the form H 0 : μ μ 0 vs. H A : μ < μ 0 then the test statistic is Z = ¯ X μ 0 s/ n and we reject H 0 if Z < z α . The type I error will be no larger than α . Principles of Statistics 1 Lecture 12: Math 203 – p. 3/3

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Two-sided hypotheses In general, if we have the hypotheses of the form H 0 : μ = μ 0 vs. H A : μ negationslash = μ 0 Principles of Statistics 1 Lecture 12: Math 203 – p. 4/3
Two-sided hypotheses In general, if we have the hypotheses of the form H 0 : μ = μ 0 vs. H A : μ negationslash = μ 0 then the test statistic is Z = ¯ X μ 0 s/ n Principles of Statistics 1 Lecture 12: Math 203 – p. 4/3

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Two-sided hypotheses In general, if we have the hypotheses of the form H 0 : μ = μ 0 vs. H A : μ negationslash = μ 0 then the test statistic is Z = ¯ X μ 0 s/ n and we reject H 0 if | Z | > z α/ 2 . The type I error will be no larger than α . Principles of Statistics 1 Lecture 12: Math 203 – p. 4/3
Small sample hypothesis tests Similar to confidence interval, if the sample size n is small then we cannot use the CLT result to approximate the distribution of ¯ X by a normal distribution.

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