sta 2006 0809_lecturenotes_5

sta 2006 0809_lecturenotes_5 - Construction of Interval...

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Unformatted text preview: Construction of Interval Estimators : pivot definition : A random variable Q ( X , θ ) is a pivotal quantity (or pivot) if the distribution of Q ( X , θ ) is independent of all parameters. Concepts 1. Interval width and precision 2. Confidence level (confidence coefficient) A. Confidence intervals for a normal mean 1. σ 2 known 2. σ 2 unknown 53 Example Let X equal the length of life of a 60-watt light bulb marketed by a certain manufacturer of light bulbs. Assume that the distribution of X is N ( μ, 1296). A random sample of n = 27 bulbs were tested until they burned out, yielding a sample mean of ¯ x = 1478 hours. Construct a 95% confidence interval for μ . 54 Example Let X equal the amount of butterfat (in pounds) produced by a typical cow during a 305-day milk production period between her first and second calves. Assume that the distribution of X is N ( μ, σ 2 ). To estimate μ a farmer measured the butterfat production for n = 20 cows yielding the following data: 481, 537, 513, 583, 453, 510, 570, 500, 457, 555, 618, 327, 350, 643, 499, 421, 505, 637, 599, 392 Construct a 90% confidence interval for μ ....
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This note was uploaded on 06/05/2011 for the course STATISTICS 2006 taught by Professor Ho during the Spring '11 term at CUHK.

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sta 2006 0809_lecturenotes_5 - Construction of Interval...

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