## Related questions with answers

Question

A hypothesis test is conducted with a $0.05$ significance level so that there is a 0.05 chance of making the mistake of rejecting a true null hypothesis. If two different independent hypothesis tests are conducted with a $0.05$ significance level, what is the possibility that both conclusions are mistakes of rejecting a true null hypothesis?

Solution

VerifiedStep 1

1 of 2Given:

$P(\text{Type I error})=0.05$

Use the multiplication rule:

$P(both)=P(\text{Type I error})\times P(\text{Type I error})=0.05\times 0.05=0.0025$

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