Question 6.20: If in fact none of the 20 formulations have any effect on we...

If in fact none of the 20 formulations have any effect on wear, what is the probability that H_0 will be rejected for one or more of them?

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We first find the probability that the right conclusion (not rejecting H_0) is made for all the formulations. For each formulation, the probability that H_0 is not rejected is 1 – 0.05 = 0.95, so the probability that H_0 is not rejected for any of the 20 formulations is (0.95)^{20} = 0.36. The probability is therefore 1 – 0.36 = 0.64 that we incorrectly reject H_0 for one or more of the formulations.

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