Econ 0160 w professor berkowitz
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Econ 0160-W, Professor Berkowitz. Lecture 1 (chapters 1 and 2) For course information click onto www.econ.pitt.edu , go to the faculty pages, click onto Daniel Berkowitz’s page and follow the links.

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Econ 0160 w professor berkowitz
Econ 0160-W, Professor Berkowitz

  • Lecture 1 (chapters 1 and 2)

  • For course information click onto www.econ.pitt.edu, go to the faculty pages, click onto Daniel Berkowitz’s page and follow the links.

  • For the next class, read over chapter 2, and do all of the problems in chapter 2 listed in problem set 1






Initial look at the data you should already know how to interpret this table
Initial look at the data:(You should already know how to interpret this table)

  • This table doesn’t tell us anything about the relationship between test scores and the STR.


Do districts with smaller classes have higher test scores? Scatterplot of test score v. student-teacher ratio

What does this figure show?


We need to get some numerical evidence on whether districts with low STRs have higher test scores – but how?


Initial data analysis compare districts with small str 20 and large str 20 class sizes
Initial data analysis: with low STRs have higher test scores – but how? Compare districts with “small” (STR < 20) and “large” (STR ≥ 20) class sizes:

1. Estimation of  = difference between group means

2. Test the hypothesis that  = 0

3. Construct a confidence interval for 


1 estimation
1. Estimation with low STRs have higher test scores – but how?


2 hypothesis testing
2. Hypothesis testing with low STRs have higher test scores – but how?


Compute the difference of means t statistic
Compute the difference-of-means with low STRs have higher test scores – but how? t-statistic:


3 confidence interval
3. Confidence interval with low STRs have higher test scores – but how?


What comes next
What comes next… with low STRs have higher test scores – but how?


Review of statistical theory
Review of Statistical Theory with low STRs have higher test scores – but how?


A population random variable and distribution
(a) Population, random variable, and distribution with low STRs have higher test scores – but how?


Population distribution of y
Population distribution of Y with low STRs have higher test scores – but how?


B moments of a population distribution mean variance standard deviation covariance correlation
(b) Moments of a population distribution: mean, variance, standard deviation, covariance, correlation


Moments ctd
Moments, ctd. standard deviation, covariance, correlation


2 random variables joint distributions and covariance
2 random variables: joint distributions and covariance standard deviation, covariance, correlation


The covariance between test score and str is negative
The covariance between Test Score and STR is negative: standard deviation, covariance, correlation

so is the correlation…


The correlation coefficient is defined in terms of the covariance
The standard deviation, covariance, correlationcorrelation coefficient is defined in terms of the covariance:


The correlation coefficient measures linear association
The correlation coefficient measures linear association standard deviation, covariance, correlation


C conditional distributions and conditional means
(c) Conditional distributions and conditional means standard deviation, covariance, correlation


Conditional mean ctd
Conditional mean, ctd. standard deviation, covariance, correlation



Distribution of y 1 y n under simple random sampling
Distribution of Y population: 1,…, Ynunder simple random sampling




The sampling distribution of when y is bernoulli p 78
The sampling distribution of when population: Yis Bernoulli (p = .78):





The sampling distribution of when n is large
The sampling distribution of when population: n is large


The law of large numbers
The population: Law of Large Numbers:


The central limit theorem clt
The population: Central Limit Theorem (CLT):



Same example sampling distribution of
Same example population: : sampling distribution of :



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