# Lesson 7: Inferences Regarding Multivariate Population Mean

This lesson deals with inference for a multivariate population mean. Similar to a univariate population, inference problems may arise in three different scenarios:

Case I: Inference problems regarding a single multivariate population

Case II: Inference problems regarding two means from a paired population

Case III: Inference problems regarding two means from two indepenent populations

All three cases are dealt with briefly in this lesson. All three cases make use of the Hotelling's T-square statistic.

This lesson plan is divided into two parts: Basic and Advanced.

#### Learning objectives & outcomes

Upon completion of the Basic lesson, you should be able to

- Use SAS to carry out Hotelling's T-square test for the null hypothesis that a population mean vector meets specifications;
- Use SAS to carry out the paired Hotelling's T-square test for the null hypothesis that two population mean vectors are equal;
- Use SAS to carry out two-sample Hotelling's T-square tests for the null hypothesis that two population mean vectors are equal;
- Compute and interpret simultaneous and Bonferroni confidence intervals;

The current version of Minitab does not support Hotelling's T-square procedures, except in a very limited setting.