1 / 5

Z-Scores (Chapter 6)

Z-Scores (Chapter 6). Equation for Z can be solved forwards or backwards : Raw score  z-score  probability Xi  Zi  probability What score is necessary to be in the top or bottom x-percentage of The distribution?

havard
Download Presentation

Z-Scores (Chapter 6)

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. Z-Scores(Chapter 6) • Equation for Z can be solved forwards or backwards: • Raw score  z-score  probability • Xi  Zi  probability • What score is necessary to be in the top or bottom x-percentage of • The distribution? • Look up the z-score associated with that probability • Probability  z-score  raw score • For proportions below • The mean, use negative • Z-scores

  2. Finding The Proportion Between A Range Of Scores • Translate the raw scores to z-scores: • If the range spans the mean, add the areas in Column B • If the range is on one side of the mean, subtract the smaller area • From the larger area (using Column C) • Use Z-scores to find either the Proportion or the Probability

  3. What Proportion OF The Population Has An IQ 90-110? μ = 100; σ = 15 • Area between mean (X=100, Z=0) and X=110 (Z=0.67) • Column B • Z=0.67 --> .2486 (Area =Probability) • Area between mean (X=100, Z=0) and X=90 (Z=-0.67) • Column B • Z=-0.67 --> .2486 (Area =Probability) • 0.2486 + 0.2486 = .4972 --> 49.72% (~50%) of Population

  4. What Proportion OF The Population Has An IQ 70-90? μ = 100; σ = 15 • Area between mean (X=100, Z=0) and X=70 (Z=-2.00) • Column C • Z=-2.00 --> 0.0228 (Area =Probability/Proportion; 2.28%) • Area between mean (X=100, Z=0) and X=90 (Z=-0.67) • Column C • Z=-0.67 --> .2486 (Area =Probability/Proportion; 24.86%) • 0.2486 - 0.0228 = .2286 --> 22.86% of Population

  5. Finding The Scores Which Define An Extreme (2-Tail) Group • What is the range of heart rates for 95% of the population? • μ = 71; σ = 9 • Upper ScoreLower Score • X = μ + Z * σ X = μ - Z * σ • = 71 + (1.96)*9 = 71 - (1.96)*9 • = 88.6 = 53.4

More Related