06 Hypothesis Examples

06 Hypothesis Examples - Hypothesis Tests and Confidence...

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1 Hypothesis Tests and Confidence Intervals for a Population Mean Hypotheses: Two-sided test Lower-tail test Upper-tail test H 0 : μ = 0 H 1 : ! 0 H 0 : ! 0 H 1 : < 0 H 0 : ! 0 H 1 : > 0 Test Statistics and Distributions under H 0 : X ~ N ( X = = 0 , ! X = / n ) if original population is normal or n is large (CLT) Z = X ! 0 " X = X ! 0 / n ~ N (0,1) standardized test statistic used when known T = X ! 0 s X = X ! 0 s / ~ t n ! 1 standardized test statistic used when unknown Data: x obs or z obs = x obs ! 0 X = x obs ! 0 / n or t obs = x obs ! 0 s X = x ! 0 s obs / n P-Values: Two-sided test Lower-tail test Upper-tail test P ( X ! x obs ) P ( X ! x obs ) or or P ( Z ! " z obs ) + P ( Z # z obs ) P ( Z ! z obs ) P ( Z ! z obs ) or or or P ( T ! " t obs ) + P ( T # t obs ) P ( T ! t obs ) P ( T ! t obs ) Decision Rule: Reject H 0 if p-value < . There is sufficient evidence to conclude that H 0 is false. or Fail to reject H 0 if p-value > . There is insufficient evidence to conclude that H 0 is false.
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2 Example: From the Fam100 sample data, can it be concluded that the average primary wage- earner income in the population of all households is higher than $34,000? Use a 5% level of significance. Hypotheses: H 0 : μ ! 34000 H 1 : > 34000 ! = .05 Minitab Output: One-Sample T: Income1 Test of mu = 34000 vs > 34000 95% Lower Variable N Mean StDev SE Mean Bound T P Income1 100 35313 8717 872 33866 1.51 0.068 Decision: Fail to reject H 0 since p-value = .068 > .05 = . There is insufficient evidence to conclude that H 0 is false. We cannot say whether the population average is higher than $34,000.
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3 Hypothesis Tests and Confidence Intervals for a Population Proportion Hypotheses: Two-sided test Lower-tail test Upper-tail test H 0 : !
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06 Hypothesis Examples - Hypothesis Tests and Confidence...

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