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I would like to know the procedure in order to find the beta risk once the hypothesis test has been made.

I am aware of the fact that it is efficient to set both alpha and beta prior to data collection, but, in this case, I was given the observations and an alpha value. I used the t-test to compare the means, and one of the requirements is to test the hypothesis that the variances are the same. From the information that I have, the p-values and F-values do not allow the rejection of the null, which makes it possible to pool the variances and calculate the t-statistic for the first hypothesis. I understand how the alpha and beta risks are pictorially represented and what they mean, but unfortunately I don't see how to get this.

The answer to this question would be useful; it would be possible to state the risk of having assumed equal variances.

Any help is highly appreciated.