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.
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.