Hypothesis Test

Hypothesis Test

1. single population

   • p-value
     • one-sided
       • p-value = P (Ȳ > ȳ| H0 true)
         • reject H0
           • p-value < α
         • fail to reject H0
           • p-value ≥ α
     • two-sided
       • p-value = 2P (Ȳ > ȳ| H0 true)
         • reject H0
           • p-value < α
         • fail to reject H0
           • p-value ≥ α
     • the strength of the evidence for HA
   • confidence interval
     • one-sided
       • L = ȳ - (Zα*σ/√n)
         • reject H0
           • null value is not inside the CI
         • fail to reject H0
           • null value is inside the CI
     • two-sided
       • CI = ȳ ± (Z_(α/2)*σ /√n)
         • reject H0
           • null value is not inside the CI
         • fail to reject H0
           • null value is inside the CI
     • the range of likely values for the effect
   • hypothesis testing
     • one-sided
       • Zs = test statistic Zα = critical value
         • reject H0
           • Zs > Zα
         • fail to reject H0
           • Zs ≤ Zα
     • two-sided
       • Zs = test statistic Zα/2 = critical value
         • reject H0
           • |Zs| > Zα/2
         • fail to reject H0
           • |Zs| ≤ Zα/2
     • gives yes/no answer

2. two populations

   • p-value
     • p-value = 2P (Ȳ1 - Ȳ2 > ȳ1 - ȳ2| H0 true)
       • reject H0
         • p-value < α
       • fail to reject H0
         • p-value ≥ α
   • confidence interval
     • (ȳ1 - ȳ2) ± Zα/2 * √{ [ (σ1)^2 / n1] + [(σ2)^2 / n2]}
       • reject H0
         • 0 is not inside the CI
       • fail to reject H0
         • 0 is inside the CI
   • hypothesis testing