DOC PREVIEW
UT Knoxville STAT 201 - Chapter 05 Student 0517

This preview shows page 1-2-3-23-24-25-26-46-47-48 out of 48 pages.

Save
View full document
View full document
Premium Document
Do you want full access? Go Premium and unlock all 48 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 48 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 48 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 48 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 48 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 48 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 48 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 48 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 48 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 48 pages.
Access to all documents
Download any document
Ad free experience
Premium Document
Do you want full access? Go Premium and unlock all 48 pages.
Access to all documents
Download any document
Ad free experience

Unformatted text preview:

Slide 1Slide 2Tallest Living HumansSlide 4The Standard Deviation as a RulerStandardizing with z-scoresStandardizing with z-scoresStandardizing with z-scores (cont.)Slide 9Units of Measure and z-ScoresDifferent Units of Measure and z-ScoresSlide 12When Is a z-score BIG?When Is a z-score Big? (cont.)Slide 15Slide 16When Is a z-score Big? (cont.)When is a z-score Big? (cont.)The 68-95-99.7 RuleThe 68-95-99.7 Rule (cont.)So, When Is a z-score Big?Working with Normal ModelsSlide 23Beyond the 68-95-99.7 RuleFinding Normal Percentages Using TechnologyFinding Normal Percentages Using TechnologyFinding Normal Percentages Using Technology (cont.)Verifying the 68-95-99.7 RuleIn-Class Activity – Groups of 2 (or 3)In-Class Activity (cont.)In-Class Activity (cont.)In-Class Activity (cont.)In-Class Activity (cont.)Given an Area, What is y?In-Class Activity (cont.)Slide 36Slide 37Are You Normal? Normal Probability Plots (cont)Are You Normal? Normal Probability Plots (cont)Slide 40How Straight is “Straight Enough”?Goodness of Fit TestGoodness of Fit Test (Cont.)Goodness of Fit Test (Cont.)WarningChapter Example #1Chapter Example #1, continuedChapter Example #1, continued1Chapter05 Presentation 0517Copyright © 2014, 2012, 2009 Pearson Education, Inc.Chapter 5The Standard Deviation as a Ruler and the Normal Model2Chapter05 Presentation 0517Copyright © 2014, 2012, 2009 Pearson Education, Inc.5.1Standardizing with z-ScoresChapter05 Presentation 05173Copyright © 2014, 2012, 2009 Pearson Education, Inc.Tallest Living HumansRecent research estimates that the average height of men is 5’ 9” (69 inches) with a standard deviation of 3.0 inches. For women, the average is 5’ 3.5” (63.5 inches) with a standard deviation of 2.5 inches.Chapter05 Presentation 05174Copyright © 2014, 2012, 2009 Pearson Education, Inc.According to 2011 Edition of Guiness World Records, the tallest living man is Sultan Kösen of Turkey. He stands 8’ 3.0” (99.0 inches). The tallest living woman is Yao Defen of China. She stands 7’ 8.0” (92.0 inches).Sultan is taller than Yao, but is his height more unusual?Chapter05 Presentation 05175Copyright © 2014, 2012, 2009 Pearson Education, Inc.The Standard Deviation as a RulerThe standard deviation is the most common measure of variation.The trick in comparing very different-looking values is to use standard deviations as our rulers.Chapter05 Presentation 05176Copyright © 2014, 2012, 2009 Pearson Education, Inc.Standardizing with z-scoresWe compare individual data values to their mean, relative to their standard deviation using the following formula:z tells us how many standard deviations the value y is away from the mean. z y  y sChapter05 Presentation 05177Copyright © 2014, 2012, 2009 Pearson Education, Inc.Standardizing with z-scoresChapter05 Presentation 05178Copyright © 2014, 2012, 2009 Pearson Education, Inc.Standardizing with z-scores (cont.)Calculate z-scores for Sultan (y=99.0”) and Yao (y=92.0”). Recall, for our Height example:Men WomenMean 69” 63.5”Std. Dev.3” 2.5”9Chapter05 Presentation 0517Copyright © 2014, 2012, 2009 Pearson Education, Inc.5.2Shifting and ScalingChapter05 Presentation 051710Copyright © 2014, 2012, 2009 Pearson Education, Inc.Units of Measure and z-ScoresIf you convert an entire data set into z-scores:This is known as standardizing the data.The z-scores are unitless numbers.This shifts the mean to 0, andThis rescales the standard deviation to 1.Shifting and rescaling a data set does not change the shape of the distribution.This applies to converting data into z-scores, or converting data from one unit of measure to another.Chapter05 Presentation 051711Copyright © 2014, 2012, 2009 Pearson Education, Inc.Different Units of Measure and z-ScoresDaily high temperature in Knoxville, TN from 05/01/08 to 05/31/08 in Fahrenheit (F°) and Celsius (C°).Calculate the Z-scores for the maximum values:C° = 5(F° - 32)9Z = Z =12Chapter05 Presentation 0517Copyright © 2014, 2012, 2009 Pearson Education, Inc.5.3Normal ModelsChapter05 Presentation 051713Copyright © 2014, 2012, 2009 Pearson Education, Inc.When Is a z-score BIG?A z-score gives us an indication of how unusual a value is because it tells us how far it is from the mean.The z-scores for Sultan and Yao are at least 10, but these are world records (very unusual)! Where is the cutoff between typical and unusual values?Chapter05 Presentation 051714Copyright © 2014, 2012, 2009 Pearson Education, Inc.When Is a z-score Big? (cont.)There is no universal standard for z-scores, but there is a model that shows up over and over in Statistics.This model is called the Normal Model.Normal models are appropriate for distributions whose shapes are unimodal and symmetric.Chapter05 Presentation 051715Copyright © 2014, 2012, 2009 Pearson Education, Inc.This is a histogram of the heights (in inches) of 1500 women (mean 63.5”, standard deviation 2.5”) with a Normal model drawn on top of it.Chapter05 Presentation 051716Copyright © 2014, 2012, 2009 Pearson Education, Inc.This is the same histogram, showing where Yao Defen’s height falls (recall, her height was z=11.4 standard deviations above the mean). 92.0”Chapter05 Presentation 051717Copyright © 2014, 2012, 2009 Pearson Education, Inc.When Is a z-score Big? (cont.)There is a Normal model for every possible combination of mean and standard deviation. We write N(μ,σ) to represent a Normal model with a mean of μ and a standard deviation of σ.When we standardize Normal data, we still call the standardized value a z-score, and we write yzms-=Chapter05 Presentation 051718Copyright © 2014, 2012, 2009 Pearson Education, Inc.When is a z-score Big? (cont.)Once we have standardized, we need only one Normal model: The N(0,1) model is called the Standard Normal Model (or the Standard Normal Distribution).Chapter05 Presentation 051719Copyright © 2014, 2012, 2009 Pearson Education, Inc.The 68-95-99.7 RuleWe will be more precise in the near future, but until then we will use a simple rule that tells us a lot about the Normal model.On exams, be very familiar with this rule!Chapter05 Presentation 051720Copyright © 2014, 2012, 2009 Pearson Education, Inc.The 68-95-99.7 Rule (cont.)The following shows what the 68-95-99.7 Rule tells us:mm +m +m +mmmChapter05 Presentation 051721Copyright © 2014, 2012, 2009 Pearson Education, Inc.So,


View Full Document

UT Knoxville STAT 201 - Chapter 05 Student 0517

Documents in this Course
Chapter 8

Chapter 8

43 pages

Chapter 7

Chapter 7

30 pages

Chapter 6

Chapter 6

43 pages

Chapter 5

Chapter 5

23 pages

Chapter 3

Chapter 3

34 pages

Chapter 2

Chapter 2

18 pages

Chapter 1

Chapter 1

11 pages

Load more
Download Chapter 05 Student 0517
Our administrator received your request to download this document. We will send you the file to your email shortly.
Loading Unlocking...
Login

Join to view Chapter 05 Student 0517 and access 3M+ class-specific study document.

or
We will never post anything without your permission.
Don't have an account?
Sign Up

Join to view Chapter 05 Student 0517 2 2 and access 3M+ class-specific study document.

or

By creating an account you agree to our Privacy Policy and Terms Of Use

Already a member?