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Simulated Experiments
To perform the hypothesis test, we determine whether the closest distance of the first trial, the trial associated with the data under test, lies in the critical region, i.e. whether or not it is less than or equal to .005513. If yes, we reject the Null hypothesis in favor of the Alternative. If no, we reject the Alternative hypothesis in favor of the Null hypothesis. The smallest distance between point set 1 and point set 2 is .004344. Since .004344 is less than the critical value .005513 we reject the Null hypothesis in favor of the Alternative hypothesis.
Red denotes points from point set 1. Green denotes points from point set 2. This is the plot of the first trial which by construction has point set 2 moved closer to point set 1. The smallest distance between point set 1 and point set 2 is .004344