ec41lecture10_handout

ec41lecture10_handout - Statistics for Economists Lecture...

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Statistics for Economists Lecture 10 Kata Bognar UCLA Normal Approximations to the Binomial Distribution Population and Sampling Distribution Sums of Random Variables Distribution of the Sample Mean Mean of the Sample Mean Statistics for Economists Lecture 10 Kata Bognar UCLA May 4, 2010
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Statistics for Economists Lecture 10 Kata Bognar UCLA Normal Approximations to the Binomial Distribution Population and Sampling Distribution Sums of Random Variables Distribution of the Sample Mean Mean of the Sample Mean Announcements Homework 3 is due on Thursday, May 6 Homework 4 will be posted on Thursday Class feedback
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Statistics for Economists Lecture 10 Kata Bognar UCLA Normal Approximations to the Binomial Distribution Population and Sampling Distribution Sums of Random Variables Distribution of the Sample Mean Mean of the Sample Mean Last Lecture Continuous random variables Normal distribution
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Statistics for Economists Lecture 10 Kata Bognar UCLA Normal Approximations to the Binomial Distribution Population and Sampling Distribution Sums of Random Variables Distribution of the Sample Mean Mean of the Sample Mean Today’s Outline 1 Normal approximation to the binomial distribution 2 Sampling distribution, sampling error 3 Sums of random variables, random sampling 4 Sampling distribution of the sample mean 5 Readings: Weiss, Chapter 6.5, 7.1 - 7.2 6 Readings for next class: Weiss, Chapter 7.2 - 7.3
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Statistics for Economists Lecture 10 Kata Bognar UCLA Normal Approximations to the Binomial Distribution Population and Sampling Distribution Sums of Random Variables Distribution of the Sample Mean Mean of the Sample Mean Normal Approximation to the Binomial Distribution Recall the binomial probability formula: P ( X = x ) = n x p x (1 - p ) n - x . If n is large, it may be difficult to calculate P ( X = x ) . If n is large and p is close to 0 . 5, a normal curve with μ = np σ = p np (1 - p ) is a good approximation of the binomial histogram. If both np > 5 and n (1 - p ) > 5 , we can use probabilities corresponding to a normal distribution to approximate binomial probabilities.
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Statistics for Economists Lecture 10 Kata Bognar UCLA Normal Approximations to the Binomial Distribution Population and Sampling Distribution Sums of Random Variables Distribution of the Sample Mean Mean of the Sample Mean Normal Approximation... - Example Consider Example 6.18. A random variable X follows a binomial distribution with parameters n = 10 and p = 0 . 5 . The probability that X is either 7 or 8 is P ( X = 7) + P ( X = 8) = 0 . 1172 + 0 . 0439 = 0 . 1611 .
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Statistics for Economists Lecture 10 Kata Bognar UCLA Normal Approximations to the Binomial Distribution Population and Sampling Distribution Sums of Random Variables Distribution of the Sample Mean Mean of the Sample Mean Normal Approximation... - Example (cont.) A random variable Y that follows a normal distribution with μ = np = 5 σ = p np (1 - p ) = 2 . 5 = 1 . 58 is a good approximation of X .
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