ch14estimationofmean,varianceandproportion

45 xi x 2 n 1 712 6145 596 6145

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: al to it’s degrees of freedom. E ( χ k2 ) = k Conclusion: E(s²)=σ² Therefore the sample variance, s², is an UNBIASED estimator of the population variance, σ². ( xi − x ) 2 ∑ i =1 n n n 2 σ 2 χ n −1 ~ n 2 σ 2 χ n −1 } = E( ) n E{ i =1 ( xi − x ) 2 ∑ n σ2 2 = E ( χ n −1 ) n σ2 = ⋅ (n − 1) n ≠σ2 Conclusion: E(s²) is NOT EQUAL to σ² Therefore this estimator is NOT an UNBIASED estimator of the population variance, σ². IT is BIASED! Example 2: For the following data 71.2, 60.0, 55.3, 65.4, 32.7, 78.6, 68.8, 59.6 estimate σ². estimate Solution: x = 61.45 ( xi − x ) 2 ∑ n −1 = (71.2 − 61.45) + ....... + (59.6 − 61.45) 8 −1 ˆ σ 2 = s2 = = 189.8171 D. Estimation of σ ˆ σ 2 = s2 While is an unbiased estimate for σ², we usually use to estimate σ. ˆ σ...
View Full Document

This note was uploaded on 02/22/2010 for the course FBE STAT0302 taught by Professor Unknown during the Spring '10 term at HKU.

Ask a homework question - tutors are online