Probstat/week15 practice 1

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This is part of probstat.

Data generation

Generate 5 sets of samples from normal populations, each of size 10, on a spreadsheet software. Make sure that the mean and variance of each set can be modified easily.

Prob-anova-data.png

Variance estimations

Estimator 1. The first estimator for is

This estimator is always correct. (Even when is not true.)

Estimator 2. The second estimator is calculated from the sample means. It will be correct only when is true.

Hypothesis testing

Then compute

and

Recall that

,

and

.

Also, since is independent of , and are independent. Thus, the statistic

Therefore, we can use the table for the F-distribution to test for .