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Unformatted text preview: ! X 2i , i = 1, 2,…, n D!0
sD / n for large n (CLT) standardized test statistic ~ tn!1 Data:
dobs or tobs = dobs ! µ D 0 sD = dobs ! 0
sD / n P-Values:
Two-sided test P(T ! " tobs ) + P(T # tobs ) Lower-tail test
P( D ! dobs ) Upper-tail test
P( D ! dobs ) 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.
Fail to reject H 0 if p-value > ! . There is insufficient evidence to conclude that H 0 is false. 7 Example: From the Fam100 sample data, can it be concluded that the average primary income
is higher than the average secondary income in the population of all households? Use a 1% level
Hypotheses: H 0 : µ Inc1 ! µ Inc 2 " 0 ! = .01 H1 : µ Inc1 ! µ Inc 2 > 0 Minitab Output:
Paired T- Test and CI: Income1, Income2
Paired T for Income1 - Income2
13306 SE Mean
1331 99% lower bound for mean difference: 20723
T-Test of mean difference = 0 (vs > 0): T-Value = 17.94 P-Value = 0.000 Decision: Reject H 0 since p-value = .000 < .01 = ! . There is sufficient evidence to conclude
that H 0 is false. The average Income1 is higher than average Income2 in the population.
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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.
- Spring '13