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Exam 3 - Study Sheet, Cheat Sheet of Statistics

Math 1530-03, Rodger Green III

Typology: Cheat Sheet

2022/2023

Uploaded on 10/15/2024

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Chapter 7
TheCentral Limit Theorem for Means, and theCentral Limit Theorem for Sums. Both
are concerned with drawing finite samples (with sizen) from a population with a known mean
(μ) and standard deviation (σ).
Central Limit Theorem of Means:
1. The normal distribution has thesame meanas the original distribution.
2. The normal distribution has a standard deviation that is equal to the original standard
deviation (σ) divided by the square root of the sample size (√𝑛).
NOTE: The variablenis the number of values that are averaged together, not the number
of times the experiment is done.
Central Limit Theorem for Sums:
The Central Limit Theorem for Sums states that the mean of the normal distribution of
sumsis equal to:
(n)(μX)=(150)(7.2)=1080
.
The Central Limit Theorem for Sumsstates the standard deviation of the normal
distribution of sums equal to:
(σX)(
n)=
(
1.2
)
(
150
)
14.70
Input the parameters into thenormalcdf()function asfollows: normalcdf(85,92,0,15/√31)as the
format for normalcdf function is normalcdf(lower value, upper value,μ,𝜎/√𝑛). After pressing
enter, thecalculator displays a value closer to0.7368.
Chapter 12
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Chapter 7 The Central Limit Theorem for Means, and the Central Limit Theorem for Sums. Both are concerned with drawing finite samples (with size n) from a population with a known mean (μ) and standard deviation (σ). Central Limit Theorem of Means:

  1. The normal distribution has the same mean as the original distribution.
  2. The normal distribution has a standard deviation that is equal to the original standard deviation (σ) divided by the square root of the sample size (√𝑛). NOTE: The variable n is the number of values that are averaged together, not the number of times the experiment is done. Central Limit Theorem for Sums: The Central Limit Theorem for Sums states that the mean of the normal distribution of sums is equal to: ( n )( μX )=( 150 )(7.2)= 1080. The Central Limit Theorem for Sums states the standard deviation of the normal

distribution of sums equal to: ( σ X )(√ n )=(^ 1.2)^ (^ √ 150 )^ ≈ 14.

Input the parameters into the normalcdf() function as follows: normalcdf(85,92,0,15/√31) as the format for normalcdf function is normalcdf(lower value, upper value, μ, 𝜎/√𝑛). After pressing enter, the calculator displays a value closer to 0.7368.

Chapter 12

Linear regression: Examples The regression equation is y hat Value = 441.0 - 27.15*Age, Where: S = 21.7349 R-Sq = 85.6%. Calculate r as √0.856 = -0.9254 and the sign is negative because the slope is negative. Vocabulary terms Regression; regression line; regression equation: ŷ= a + bx = bx + a (in text). Slope of line = b (in text). y intercept = a (in text). y is the OBSERVED value). y hat (or y ̂ ) is the PREDICTED value. Table of synonyms

x y

Independent Dependent

Explanatory Response

Predictor Predicted

Input Output/outcome

Cause Effect

Correlation: Correlation coefficient (aka “r” value aka Pearson number) Coefficient of determination (aka r^2 value)

Outliers Review: three types:  Regression line outliers  B/W plot outliers  Normal curve outliers Showing association:  categorical vs categorical  categorical vs quantitative  quantitative vs quantitative