Inferential statistics

N O A = 2 0 -2 O 8 1. find the eigenvalues and obtain the orthogonal eigenvectors. 2. find the spectral decomposition of A. 3. find A-1 4. Prove that A1/2A-1/2 = A-1/2A1/2 = 1Formulas for Inferential Statistics estimate - parameter Standardized test statistic: standard deviation of estimate Confidential interval: estimate + (critical value) . (standard deviation of estimate) Single-Sample Statistic Standard Deviation Mean p(1- p) Proportion Two-Sample Statistic Standard Deviation Difference of means (unequal variances) 2 Difference of means (equal variance) 1 + Difference of proportions [unequal variance) p(I-p) p,(-p ) Difference of proportions (equal variance) Vp(1- p) 1 1 Chi-square test statistic = $- (observed - expected) expectedLet {Xiji=1 36 be the sequence of continuous IIDRV with EXi = 40, Var Xi = 144, i = 1, ..., 36 and A36 Eil Xi = 36 (a) By using the Markov's inequality estimate P( A36