1 / 22

Decision Making (2 Samples)

Decision Making (2 Samples). Introduction of 2 samples. 5-2 Inference on the Mean of 2 population, Variance known. Inference on the Mean of 2 population, Variance known.

dixon
Télécharger la présentation

Decision Making (2 Samples)

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Decision Making (2 Samples)

  2. Introduction of 2 samples

  3. 5-2 Inference on the Mean of 2 population, Variance known

  4. Inference on the Mean of 2 population, Variance known

  5. Ex: Drying time of primer has SD=8 min. 10 Samples of Primer1has x-bar1=121 min. and another 10 samples of Primer II has x-bar2=112 min. Is the primer 2 has effect to drying time. • H0: 1-2=0 H1:1-2>0 • n1=n2 1=2 • Z0=2.52 • P=1-(2.52)=0.0059 <0.05 • Then reject H0

  6. Sample size

  7. 5-3 Inference on the Mean of 2 population, Variance unknown

  8. Case I: Equal variances (Pooled t-test)

  9. H0: 1-2=0 H1:1-2≠0 • n1=n2=8 1=2 • T0=-0.35 • P=0.729 > 0.05 • Then accept H0 Two-Sample T-Test and CI: C5, C8 N Mean StDev SE Mean C5 8 92.26 2.39 0.84 C8 8 92.73 2.98 1.1 Difference = mu (C5) - mu (C8) Estimate for difference: -0.48 95% CI for difference: (-3.37, 2.42) T-Test of difference = 0 (vs not =): T-Value = -0.35 P-Value = 0.729 DF = 14 Both use Pooled StDev = 2.7009

  10. 5-3 Inference on the Mean of 2 population, Variance unknown

  11. H0: 1-2=0 H1:1-2≠0 • n1=n2=10 1 ≠ 2 • T0=-2.77 • P=0.016 < 0.05 • Then reject H0 Two-Sample T-Test and CI: Metro, Rural N Mean StDev SE Mean Metro 10 12.50 7.63 2.4 Rural 10 27.5 15.3 4.9 Difference = mu (Metro) - mu (Rural) Estimate for difference: -15.00 95% CI for difference: (-26.71, -3.29) T-Test of difference = 0 (vs not =): T-Value = -2.77 P-Value = 0.016 DF = 13

  12. 5-4 Paired t-test • A special case of the two-sample t-tests of Section 5-3 occurs when the observations on the two populations of interest are collected inpairs. • Each pair of observations, say (X1j, X2j), is taken under homogeneous conditions, but these conditions may change from one pair to another. • For example; The test procedure consists of analyzing the differences between hardness readings on each specimen.

  13. Paired t-test

  14. H0: D=1-2=0 H1: D= 1-2≠0 • n1=n2=9 1 ≠ 2 • T0=6.08 • P=0.000 < 0.05 • Then reject H0 Paired T-Test and CI: Karlsruhe method, Lehigh method N Mean StDev SE Mean Karlsruhe method 9 1.3401 0.1460 0.0487 Lehigh method 9 1.0662 0.0494 0.0165 Difference 9 0.2739 0.1351 0.0450 95% CI for mean difference: (0.1700, 0.3777) T-Test of mean difference = 0 (vs not = 0): T-Value = 6.08 P-Value = 0.000

  15. 5-6 Inference on 2 population proportions

  16. Inference on 2 population proportions

  17. H0: p1=p2 H1: p1≠p2 • Z0=5.36 • P=0.000 < 0.05 • Then reject H0 Test and CI for Two Proportions Sample X N Sample p 1 253 300 0.843333 196 300 0.653333 Difference = p (1) - p (2) Estimate for difference: 0.19 95% CI for difference: (0.122236, 0.257764) Test for difference = 0 (vs not = 0): Z = 5.36 P-Value = 0.000

More Related