STAT1051_inference_lesson2(1)

# STAT1051_inference_lesson2(1) - Confidence Interval...

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1 Confidence Interval Estimating the Mean: Large Sample

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2 Example 1.0: The seasonal rainfall in a county in California, when observed over sixteen randomly picked years, yielded a mean rainfall of 20.8 inches. From the past experience, rainfall during a season is normally distributed with σ = 2.8 inches. Construct a 90% and 95% confidence intervals for the true mean.
3 Example 1.0 (cont) Here n = 16; Sample mean = 20.8 ; σ = 2.8. Though the sample size is small, since σ is known and that the population ( Rainfall during a season) is normally distributed all conditions are satisfied. X For 90% confidence interval, z * = 1.645

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4 / 2 X z n α σ         ± (19.65, 21.95) Example 1.0 (cont) Hence 90% confidence interval for the mean is given by 2.8 20.8 (1.65) 16 ± In particular the 90% confidence interval is
5 Solution 1.0 (cont) 95% confidence interval for mean: z * = 1.96 2.8 20.8 (1.96) 16 ± Hence 95% confidence interval for the mean is = (19.43, 22.17)

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## This note was uploaded on 11/27/2011 for the course STAT 1051-10 taught by Professor Balaji during the Fall '11 term at GWU.

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STAT1051_inference_lesson2(1) - Confidence Interval...

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