You read that a statistical test at the a 0. 01 level has probability 0. 14 of making a type ii error when a specific alternative is true. What is the power of the test against this alternative?

The power of the test against the specific alternative is given by 1 minus the probability of making a Type II error. Therefore, the power is 0.86= 86%

In statistical hypothesis testing, the power of a test is the probability that it correctly rejects a null hypothesis when a specific alternative hypothesis is true. In this case, we are given that the test has a significance level of α = 0.01, which means that the test rejects the null hypothesis if the probability of obtaining the observed result, or one more extreme, under the null hypothesis is less than 0.01.

However, we also know that when a specific alternative hypothesis is true, the test has a probability of making a Type II error of 0.14. This means that there is a 14% chance that the test fails to reject the null hypothesis, even though the alternative hypothesis is true.

Therefore, the power of the test against this specific alternative hypothesis is given by 1 minus the probability of making a Type II error, which is:

Power = 1 - P(Type II error) = 1 - 0.14 = 0.86

So, the power of the test against the specific alternative hypothesis is 0.86 or 86%. This means that when the alternative hypothesis is true, the test correctly rejects the null hypothesis 86% of the time.

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