# Segment 12 Sanmit Narvekar

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## Segment 12

#### To Calculate

1. What is the critical region for a 5% two-sided test if, under the null hypothesis, the test statistic is distributed as $\displaystyle \text{Student}(0,\sigma,4)$ ? That is, what values of the test statistic disprove the null hypothesis with p < 0.05? (OK to use Python, MATLAB, or Mathematica.)

Thus, values of the test statistic greater than 2.776 sigma or less than -2.776 sigma disprove the null hypothesis using a 2-tailed pvalue test at the 5% significance level.

2. For an exponentially distributed test statistic with mean $\displaystyle \mu$ (under the null hypothesis), when is the the null hypothesis disproved with p < 0.01 for a one-sided test? for a two-sided test?

And again via Mathematica:

The first row corresponds to a 1 tailed test. The other two are for 2-tailed tests.