Question 6.19: Given that H0 was rejected for one of the 20 formulations, i......

ISE Principles of Statistics for Engineers and Scientists [987713]

Given that $H_{0}$ was rejected for one of the 20 formulations, is it plausible that this formu-lation actually has no effect on wear?

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Yes. It is plausible that none of the formulations, including the one for which $H_{0}$ was rejected, have any effect on wear. Twenty hypothesis tests were made. For each test there was a 5% chance (i.e., 1 chance in 20) of a type I error. We therefore expect on the average that out of every 20 true null hypotheses, one will be rejected. So rejecting $H_{0}$ in one out of the 20 tests is exactly what one would expect in the case that none of the formulations made any difference.

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