Inferences on Variance

Inferences on Variance - Section 4.6 Page 1 Inferences on...

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Unformatted text preview: Section 4.6 Page 1 Inferences on Variance Sample Variance, s 2 h s 2 is the most efficient point estimator for σ 2 when a sample of size n is drawn from a normal population. h What do we know about the distribution of s 2 ? h g G ¡ ¢£¤¥¦§ ¨ © ¨ follows a chi-squared distribution with n-1 degrees of freedom when a sample is taken from a normal distribution. Chi-Squared Distribution 5 10 15 20 25 0.0 0.1 0.2 0.3 0.4 0.5 Chi-squared value df=2 df=5 df=10 Section 4.6 Page 2 Confidence Intervals and Hypothesis Testing for Estimate of the Variance g G¡ ¢£¤ ¥ ⁄ ¥ ¦ §¨ © 1ª« ¥ ¬ ¥ ¦ ¡ ¤ ¥ ⁄ ¥ ­ ® 1 © ¯ (1-α)100% Confidence Interval for σ 2 If s 2 is the variance of a random sample of size n from a normal population, α (1-α)100 % confidence interval for σ 2 is §¨ © 1ª« ¥ ¡ ¤ ¥ ⁄ ¥ ¦ ¬ ¥ ¦ §¨ © 1ª« ¥ ¡ ¢£¤ ¥ ⁄ ¥ where ¡ ¢£¤ ¥ ⁄ ¥ and ¡ ¤ ¥ ⁄ ¥ are the χ 2 values with df = n – 1 degrees of freedom, leaving areas of 1- α/2 and α/2, respectively, to the right. Section 4.6 Section 4....
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Inferences on Variance - Section 4.6 Page 1 Inferences on...

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