Overview Section
In this lesson, we consider the properties of the sample mean vector and the sample correlations which we had defined earlier. We will also consider estimation and hypothesis testing problems on the population mean and correlation coefficients.
This lesson will explore the following questions...
Sample Mean Vectors
- What is the distribution of \(\bar{x}\) when data come from a multivariate normal distribution?
- What are the properties of \(\bar{x}\) when data do NOT come from a multivariate normal distribution but the sample size n is large
- How to construct a confidence interval for a single multivariate normal population mean
- How to construct confidence intervals for several multivariate normal population means simultaneously
Sample Correlations
- How can we test the null hypothesis that there is zero correlation between two variables?
- What can we conclude from such hypothesis tests?
- How can we assess uncertainty regarding estimated correlation coefficients using confidence intervals?
- What is the appropriate interpretation for confidence intervals?
Objectives
Upon completion of this lesson, you should be able to answer the following questions:
- Describe the distribution of \(\bar{x}\) when data come from a Multivariate Normal distribution
- Construct simultaneous confidence intervals for several multivariate normal population means
- Conduct hypothesis testing on the correlation between two variables
- Assess confidence intervals for correlation between two variables