The power of a significance test to reject the null hypothesis when a particular value of the alternative is true is 0.8. What is the probability that this test results in a Type II error?

Power is the probability of correctly rejecting the null hypothesis when the specified alternative is true. The probability of a Type II error, β, is the chance of failing to reject the null in that situation, so β = 1 − 0.8 = 0.20. Therefore, the correct choice is 0.20.

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