notes10 - Stat 430/Math468 Notes #10 Inference about a Mean...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Stat 430/Math468 – Notes #10 Chapter 5 Inference about a Mean Vector Suppose are random sample from a normal population . The sample mean and sample variance-covariance matrix are, respectively, 1 ,..., n XX (, ) p N μΣ 1 12 ( ... ) n n =+ + + X X and 1 1 1 () n jj n j = =− SX X X ' X . Hypotheses: 00 : H = μμ vs , where 0 : a H 10 ( ,..., )' p μ = μ Test statistic: Hotelling’s 21 ' ( Tn X μ μ ) Null distribution: Under , 0 H 2 , (1 ) ~ pn p np T F . [Equivalently, 2 , ~ ) TF ] Decision Rule (Critical value method. For P-value method, see remark 1.): Suppose the observed sample mean vector is x and sample variance-covariance matrix is . Then at significance level S α , reject if 0 H , ) ' ( F ) −> x μ Sx μ where , F is the upper 100 th percentile of the , F distribution. Remark : 1. Suppose the observed is . Then the P-value = 2 T 2 obs t 2 , ) obs PF t ⎛⎞ > ⎜⎟ ⎝⎠ . 2. is invariant under linear transformation of the data (e.g. changing the units of measurements: 2 T o F Æ o C).
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 6

notes10 - Stat 430/Math468 Notes #10 Inference about a Mean...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online