x =matrix(c(-3,4,5,15,16,11),nrow = 3, ncol = 2) mu = matrix(c(9,5),nrow = 2) # Hypothesis matrix

HotT2 = function(x,mu,a){

xbar = colMeans(x) # Mean Vector s = var(x) # Variance Covariance Matrix s_in = solve(s) # inverse of variance covariance matrix n = nrow(x) p = ncol(x) X = xbar-mu t = n%%t(X)%%s_in%*%(X) #Hotelling T-Squared

print("mean vector is ",quote = FALSE) print (xbar) print("variance covarinace matrix is ",quote = FALSE) print(s) print(paste("calculated value of Hotelling T-squared is ", t),quote = FALSE)

decision = function(alp,n,p){ f = ((n-1)p)/(n-p)qf(alp,(n-1),(n-p)) print(paste("Critical value of f statistic with df",n-1,"and",n-p,"is",f),quote = FALSE) print(f) if (t>f) { print(paste("At",a100,"% level of significance we reject our null hypothesis that true mean is not equal to"),quote = FALSE) print(mu) } else { print(paste("At",a100,"% level of significance we cannot reject our null hypothesis that true mean is not equal to"),quote = FALSE) print(mu) } } decision(a,n,p) }

HotT2(x,mu,a=0.90)