A multivariate hypothesis test of difference between a vector of sample means and a vector of true means (mu). The null hypothesis assumes no differences for each pair of sample mean and true mean, the alternative hypothesis assumes not all pairs are equal. Smaller p-value would reject the null hypothesis. The distribution under the null hypothesis is an approximation to Hotelling's T^2 distribution, hence the test is an approximated test.
A multivariate method that is the multivariate counterpart of Student's t and which also forms the basis for certain multivariate control charts is based on Hotelling's T2 distribution, which was introduced by Hotelling (1947).
Hotelling, H. (1947). Multivariate Quality Control. In C. Eisenhart, M. W. Hastay, and W. A. Wallis, eds. Techniques of Statistical Analysis. New York: McGraw-Hill.