{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

PSLS.PPT.Ch18

# PSLS.PPT.Ch18 - populationmeans(unknown PSLS chapter 18...

This preview shows pages 1–7. Sign up to view the full content.

Two-sample problems for  population means  ( σ  unknown) PSLS chapter 18 © 2009 W.H. Freeman and Company

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

View Full Document
Objectives (PSLS chapter 18) Comparing two means (σ unknown) t -distribution for two independent samples Two-sample t test Two-sample t confidence interval Robustness Details of the two sample t procedures
t  distribution for 2 independent samples We have 2 independent SRS coming from 2 populations with ( μ 1 , σ 1 ) and ( μ 2 , σ 2 ) unknown. We use ( 1 , s 1 ) and ( 2 , s 2 ) to estimate ( μ 1 , σ 1 ) and ( μ 2 , σ 2 ) respectively. Both populations should be Normally distributed. In practice, it is enough that both distributions have similar shapes and that the sample data contain no strong outliers. x x

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

View Full Document
SE = s 1 2 n 1 + s 2 2 n 2 s 1 2 n 1 + s 2 2 n 2 df μ 1 μ 2 x 1 - x 2 The two-sample t statistic follows approximately the t distribution with a standard error SE (spread) reflecting variation from both samples: df ≥ smallest of ( n 1 , n 2 ) - 1 “smallest of ( n 1 , n 2 ) - 1” is a conservative approximation ; use it for hand-computations
t = ( x 1 - x 2 ) - ( μ 1 - μ 2 ) SE Two-sample  t  test  H 0 : μ 1 = μ 2 < = μ 1 μ 2 = 0 with either a one-sided or a two-sided alternative hypothesis. We find how many standard errors (SE) away from ( μ 1 μ 2 ) is ( 1 2 ) by standardizing with t: Because H 0 is ( μ 1 - μ 2 29 = 0, t is simply with df ≥ smallest( n 1 , n 2 )-1 t = x 1 - x 2 s 1 2 n 1 + s 2 2 n 2 x x

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

View Full Document
Does smoking damage the lungs of children exposed to parental smoking? Forced Vital Capacity (FVC) is the volume (in milliliters) of air that an individual can exhale in 6 seconds. FVC was obtained for a sample of children not exposed to parental smoking and a sample of children exposed to parental smoking.
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 19

PSLS.PPT.Ch18 - populationmeans(unknown PSLS chapter 18...

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online