Lecture13

# Lecture13 - Lecture 13 Stat 350 7.2 Large Sample Confidence...

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Lecture 13 Stat 350 7.2 Large Sample Confidence Intervals for a population mean ( μ )

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Homework 5 Due Friday, Feb 25 Ch 7.2 (page 301 303) 7, 8, 9, 11, 12 13, 14, 15, 18, 19
Review: Point Estimate The statistic is a point estimate for population mean μ unbiased and consistent Example: Suppose we obtain a SRS of 100 plots of corn with yields (in bushels), and the mean yield is 123.8 x x 123.8

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Review: Point Estimate Example: Suppose we obtain a SRS of 100 plots of corn with yields (in bushels), and the mean yield is 123.8 Shortcoming: provides no information about the precision and reliability of estimation for μ x x 123.8
Confidence Interval An Entire Interval of Plausible Values Example: Suppose we observe 100 plots of corn with yields (in bushels) Sample Mean = 123.8 Sample Standard Deviation = 12.3 What are the plausible values for (population) mean yield of this variety of corn?

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Sampling Distribution n=100 (large), CLT => σ is unknown when n is large, σ s s is the sample standard deviation So, ) , ( ~ n N X s X s n 12.3 100 1.23
Sampling Distribution n=100 (large), CLT => Question: Find a symmetric interval ( μ - a, μ +a) around μ , so that the sample mean is in -a, μ + a) 95% of the time. X N ( ,1.23) X

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Sampling Distribution n=100 (large), CLT => P(-1.96 <Z<1.96) = 0.95 or P(-1.96 < <1.96) = 0.95 X N ( ,1.23) Z X   1.23 X   1.23

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Lecture13 - Lecture 13 Stat 350 7.2 Large Sample Confidence...

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