# Eleisha's Segment 19: The Chi-Square Statistic

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To Calculate

1. Prove the assertion on lecture slide 5, namely that, for a multivariate normal distribution, the quantity $\displaystyle ({\mathbf x-\mathbf\mu})^T{\mathbf\Sigma}^{-1}({\mathbf x-\mathbf\mu}),$ where $\displaystyle \mathbf x$ is a random draw from the multivariate normal, is $\displaystyle \chi^2$ distributed.

To Think About

1. Why are we so interested in t-values? Why do we square them?

2. Suppose you measure a bunch of quantities $\displaystyle x_i$ , each of which is measured with a measurement accuracy $\displaystyle \sigma_i$ and has a theoretically expected value $\displaystyle \mu_i$ . Describe in detail how you might use a chi-square test statistic as a p-value test to see if your theory is viable? Should your test be 1 or 2 tailed?

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