{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

06 Hypothesis Examples

# 06 Hypothesis Examples - Hypothesis Tests and Confidence...

This preview shows pages 1–4. Sign up to view the full content.

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.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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.
3 Hypothesis Tests and Confidence Intervals for a Population Proportion Hypotheses: Two-sided test Lower-tail test Upper-tail test H 0 : !

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 8

06 Hypothesis Examples - Hypothesis Tests and Confidence...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online