ec41lecture12

# ec41lecture12 - Statistics for Economists Lecture 12 Kata...

This preview shows pages 1–8. Sign up to view the full content.

Statistics for Economists Lecture 12 Kata Bognar UCLA Central Limit Theorem Approximations Special Continuous Distributions Statistics for Economists Lecture 12 Kata Bognar UCLA November 9, 2010

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Statistics for Economists Lecture 12 Kata Bognar UCLA Central Limit Theorem Approximations Special Continuous Distributions Announcements Midterm solutions are online
Statistics for Economists Lecture 12 Kata Bognar UCLA Central Limit Theorem Approximations Special Continuous Distributions Last Lecture Normal distributions

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Statistics for Economists Lecture 12 Kata Bognar UCLA Central Limit Theorem Approximations Special Continuous Distributions Today’s Outline 1 Central Limit Theorem 2 Approximations 3 χ 2 and t distributions. 4 Readings: TH, Chapter 3.6 - 3.7, Chapter 3.3: p.124 - 125. Chapter 4.1: p.156 - 158. Suggested readings: WS, Chapter 7.3 W, Chapter 7.3, 6.5 5 Readings for the next class: TH, Chapter 2.5: p.82 - 83; Chapter 3.5: p.139 - 141; Chapter 4.3: p.162 - 164.
Statistics for Economists Lecture 12 Kata Bognar UCLA Central Limit Theorem Approximations Special Continuous Distributions Distribution of the Sample Mean Suppose X 1 , X 2 ,... X n is a random sample from a distribution with a mean μ and a variance σ 2 . The sample mean is ¯ X = i X i n . the sample mean is a random variable the expected value of the sample mean is E [ ¯ X ] = μ the variance of the sample mean is Var [ ¯ X ] = σ 2 / n Can we say something about the distribution of the sample mean ? Can we say something about the probability that the sampling error is in some range?

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Statistics for Economists Lecture 12 Kata Bognar UCLA Central Limit Theorem Approximations Special Continuous Distributions Sampling from a Normal Distribution Suppose that X is a normal random variable with a mean μ and a variance σ 2 and X 1 , X 2 ,... X n is a random sample from this distribution. Then the sample mean ¯ X has a normal distribution with a mean μ and a variance σ 2 n : ¯ X N ± μ, σ 2 n ² . The random variable W = ¯ X - μ σ/ n has a standard normal distribution : W = ¯ X - μ σ/ n N (0 , 1) .
Statistics for Economists Lecture 12 Kata Bognar UCLA Central Limit Theorem Approximations Special Continuous Distributions Sampling from a Normal Distribution - Example The weight of a pizza form CPK is a random variable that has a normal distribution with a mean of 16 ounces and a standard deviation of 1 ounce. Suppose you buy 4 pizzas for a party. What is the probability that the mean weight of the 4 pizzas is more than 17 . 1 ounces? Step 1:

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 21

ec41lecture12 - Statistics for Economists Lecture 12 Kata...

This preview shows document pages 1 - 8. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online