NormalCurve_ztest 14

# NormalCurve_ztest 14 - Normal Curve Introduction The normal...

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Normal Curve Introduction

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The normal curve Aka The Bell Curve; The Normal Distribution Example: Individual’s IQ scores
68.2% 95.4% 99.6% z-scores = standard deviation units

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Normal distribution Mean IQ = 100 Standard deviation = 16 Scores vary +16.0/-16.0 from the mean of 100 84 to 116 Values higher than 116 or lower than 84 are more than one standard deviation away from the mean and would be considered more “extreme” Values that are two or three standard deviations from the mean as “outliers” These very high and very low IQ people are not “typical” of the rest of the population 68% probability that a person’s IQ is between 84 and 116 95% probability that person’s IQ is between 68 and 132 99% probability that person’s IQ is between 52 and 148
Area under the curve z-table handout

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% above/below z-score Question: Using the z-table, how many people would you expect to score below a z-score of +.75? Answer: 77.34% Question: Using the z- table, how many people would you expect to score above a z- score of - 1.18? Answer: 88.10% Question: Using the z- table, how many people would you expect to score above a z- score of +1.64? Answer: 5.05% Question: Using the z- table, how many people would you expect to score above a z- score of +1.65? Answer: 4.95% Question: Using the z- table, how many people would you expect to score above a z-score of +1.645? Answer: 5%
Example One baby compared to population of babies One baby, “Kate”, takes the “My Baby Can Read” program Every dot under the curve is one baby’s reading score (babies not in the program) How does Kate (the baby in the program) compare to babies not in the program?

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Example (cont) What if the z-score for Kate’s reading score (the baby in the program) was z = 0? She is no different than babies not in the program. Her score is in the middle of the distribution of no-program kids! Her reading score is not higher (or lower) than babies who were not in the program.
SCORE -4 -2 0 2 4 0.0 0.1 0.2 0.3 0.4 34% 34% 14% 14% 2% 2% 50% The area under a normal curve

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Example (cont) What if the z-score for Kate’s reading score (the baby in the program) was… z = +.69? She scored higher than 75.49% of the no-program kids. z = +1.20? She scored higher than 88.49% of the no-program kids. z = +1.645 She scored higher than 95% of the no-program kids.
z = +.69? She scored higher than 75.49% of the no-program kids. z = +1.20? She scored higher than 88.49% of the no-program kids. z = +1.645 She scored higher than 95% of the no-program kids. How do we know that the program worked???? Maybe Kate is just a really good reader!

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## This note was uploaded on 05/26/2011 for the course PSCH 343 taught by Professor Victoriaharmon during the Spring '11 term at Ill. Chicago.

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NormalCurve_ztest 14 - Normal Curve Introduction The normal...

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