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

ISE Principles of Statistics for Engineers and Scientists [987713]

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 formula-tions 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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