Question 6.18: If only one formulation were tested, and it in fact had no e......

ISE Principles of Statistics for Engineers and Scientists [987713]

If only one formulation were tested, and it in fact had no effect on wear, what is the probability that $H_{0}$ would be rejected, leading to a wrong conclusion?

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If the formulation has no effect on wear, then 𝜇 = 100 𝜇m, so $H_{0}$ is true. Rejecting $H_{0}$ is then a type I error. The question is therefore asking for the probability of a type I error. In general, this probability is always less than or equal to the significance level of the test, which in this case is 5%. Since 𝜇 = 100 is on the boundary of $H_{0}$ , the probability of a type I error is equal to the significance level. The probability is 0.05 that $H_{0}$ will be rejected.

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