PSLS.PPT.Ch18

PSLS.PPT.Ch18 - Twosampleproblemsfor...

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

View Full Document Right Arrow Icon
    Two-sample problems for  population means  ( σ  unknown) PSLS chapter 18 © 2009 W.H. Freeman and Company
Background image of page 1

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

View Full DocumentRight Arrow Icon
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
Background image of page 2
t  distribution for 2 independent samples We have 2 independent SRS coming from 2 populations with ( μ 1 1 ) and ( 2 2 ) unknown. We use ( 1 , s 1 ) and ( 2 , s 2 ) to estimate ( 1 1 ) and ( 2 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
Background image of page 3

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

View Full DocumentRight Arrow Icon
SE = s 1 2 n 1 + s 2 2 n 2 s 1 2 n 1 + s 2 2 n 2 df μ 1 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
Background image of page 4
t = ( x 1 - x 2 ) - ( μ 1 2 ) SE Two-sample  t  test  H 0 : 1 = 2 < = 1 2 = 0 with either a one-sided or a two-sided alternative hypothesis. We find how many standard errors (SE) away from ( 1 2 ) is ( 1 2 ) by standardizing with t: Because H 0 is ( 1 - 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
Background image of page 5

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

View Full DocumentRight Arrow Icon
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
Background image of page 6
Image of page 7
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 10/07/2011 for the course BSTT 400 taught by Professor Sallyfreels during the Fall '11 term at Ill. Chicago.

Page1 / 19

PSLS.PPT.Ch18 - Twosampleproblemsfor...

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

View Full Document Right Arrow Icon
Ask a homework question - tutors are online