06 Hypothesis Examples

2 0 h1 1 2 0 h1 1 2 0 test statistics and

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Unformatted text preview: Independent Samples) Hypotheses: Two-sided test H 0 : µ1 ! µ2 = 0 Lower-tail test H 0 : µ1 ! µ2 " 0 Upper-tail test H 0 : µ1 ! µ2 " 0 H1 : µ1 ! µ2 " 0 H1 : µ1 ! µ2 < 0 H1 : µ1 ! µ2 > 0 Test Statistics and Distributions under H 0 : # 2 2 "1 " 2 & ( X1 ! X 2 ~ N % µ X ! X = µ1 ! µ2 = 0, " X ! X = + 1 2 n1 n2 ( %12 $ ' T= ( X1 ! X 2 ) ! ( µ1 ! µ2 ) ( X1 ! X 2 ) ! 0 = ~ t" 2 2 sX ! X s1 s2 1 2 + n1 n2 if X1 ~ N and X 2 ~ N standardized test statistic Data: ( x1 ! x2 )obs or tobs = ( x1 ! x2 )obs ! ( µ1 ! µ2 )0 ( x1 ! x2 )obs ! 0 = 2 2 sX ! X s1 s2 1 2 + n1 n2 P-Values: Two-sided test P(T ! " tobs ) + P(T # tobs ) Lower-tail test P( X1 ! X 2 " ( x1 ! x2 )obs ) Upper-tail test P( X1 ! X 2 " ( x1 ! x2 )obs ) or P(T ! tobs ) or P(T ! tobs ) 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. 5 Example: From the Fam100 sample data, can it be concluded that the average debt for homeowners is higher than the a...
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This note was uploaded on 02/11/2013 for the course STAT 509 taught by Professor Grey during the Spring '13 term at Alabama.

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