ec41lecture14b

# ec41lecture14b - Statistics for Economists Lecture 14 Kata...

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Unformatted text preview: Statistics for Economists Lecture 14 Kata Bognar UCLA Interval Estimation CI for the mean if standard deviation is known (z-Interval procedure) CI for the mean if standard deviation is unknown (t-Interval procedure) Statistics for Economists Lecture 14 Kata Bognar UCLA November 18, 2010 Statistics for Economists Lecture 14 Kata Bognar UCLA Interval Estimation CI for the mean if standard deviation is known (z-Interval procedure) CI for the mean if standard deviation is unknown (t-Interval procedure) Last Lecture • χ 2 and Student’s t distributions • Interval estimation Statistics for Economists Lecture 14 Kata Bognar UCLA Interval Estimation CI for the mean if standard deviation is known (z-Interval procedure) CI for the mean if standard deviation is unknown (t-Interval procedure) Today’s Outline 1 Interval estimation 2 Confidence intervals for the mean 3 Readings: TH, Chapter 3.3: p.124 - 125.; Chapter 4.1: p.156 - 158. Chapter 2.5: p.82 - 83; Chapter 3.5: p.139 - 141; Chapter 4.2: p.162 - 164. • Suggested readings: WS, Chapter 8 W, Chapter 8 4 Readings for the next class: TH, Chapter 4.3. Statistics for Economists Lecture 14 Kata Bognar UCLA Interval Estimation CI for the mean if standard deviation is known (z-Interval procedure) CI for the mean if standard deviation is unknown (t-Interval procedure) Interval Estimation - Example Suppose that the GPA of all UCLA students are normally distributed with an unknown mean, μ and a known standard deviation, σ = 0 . 5. The mean GPA for a random sample of 16 students is 3 . 2 . Provide a range so that we can be 95.44% confident that the mean GPA of all UCLA students lies in that range. • ¯ X ∼ N ( μ, . 125 2 ) • for 95.44% of all possible samples, the sample mean lies within 2 standard deviation, i.e. with 0.25 point of the population mean • the sampling error is less than 0.25 point for 95.44% of all possible samples • the confidence intervals [¯ x- . 25 , ¯ x + 0 . 25] contain the population mean for 95.44% of all possible samples • one can be 95.44% confident that the population mean lies in [3 . 2- . 25 , 3 . 2 + 0 . 25] = [2 . 95 , 3 . 45] Statistics for Economists Lecture 14 Kata Bognar UCLA Interval Estimation CI for the mean if standard deviation is known (z-Interval procedure) CI for the mean if standard deviation is unknown (t-Interval procedure) Interval Estimation • The interval estimator is a random interval that contains the parameter for a specified proportion of the possible samples. • If this proportion is 1- α then we are talking about the (1- α ) × 100% confidence level . • The confidence interval (CI) is the realization of this estimator for the given sample....
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ec41lecture14b - Statistics for Economists Lecture 14 Kata...

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