ECON2209 Lecture Notes - Lecture 11: Central Limit Theorem, Sampling Distribution, Standard Error

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Feb 22nd:
Measures of relative standing
Percentiles
Z scores
Population
x-u/sigma
Sample
x-xbar/s
Measures the number of standard deviations that a value is from the mean
Xbar is 10
Standard deviation is 4
Find the Zscore:
Z = (28-10)/4 = 4.5… so 28 is 4.5 standard deviations away from the
mean
If the distribution is symmetrical….
68% of all observations have a z score between -1 and 1
95% of all observations have a z score between -2 and 2
99% of all observations have a z score between -3 and 3
2nd, VARs (DIST), normalcdf, put in z-score
Measures of Association (aka measures of linear relationships)
Cov(x,y) = sigmaXY =
Variance is a special case of covariance
Problem with covariance? Can't say anything about the strength of the
connection!
Correlation:
Population:
Corr is between -1and 1
Ex: Cov = 132.6
Variance of X = 34.3
Sampling Distributions
Distributions of statistics (measure of a sample)
Ex: distribution of xbar
Ex: distribution of s2
Ex: distributions of p
Sampling distributions
Need 3 things:
Mean/central location:
E(xbar)= uxbar
Dispersion
Standard error is the standard deviation of a sampling
distribution
Shape: CLT (Central Limit Theorem)
CLT1: If X is normally distributed, then xbar is a normally
distributed for any n
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Document Summary

Measures the number of standard deviations that a value is from the mean. Z = (28-10)/4 = 4. 5 so 28 is 4. 5 standard deviations away from the mean. 68% of all observations have a z score between -1 and 1. 95% of all observations have a z score between -2 and 2. 99% of all observations have a z score between -3 and 3. 2nd, vars (dist), normalcdf, put in z-score. Measures of association (aka measures of linear relationships) Variance is a special case of covariance. Can"t say anything about the strength of the connection! Distributions of statistics (measure of a sample) Standard error is the standard deviation of a sampling distribution. Clt1: if x is normally distributed, then xbar is a normally distributed for any n. Clt2: if x is not normally distributed, then xbar will be approx. normally distributed if n is large (n>30) P is at least approximately normal if n is large.

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