You have set up a test of a suitably phrased null hypothesis. After analyzing the statistical underpinnings of the test and the stringency requirements you have imposed, you have determined that the probability of rejecting the null hypothesis equals 30%. The probability that you will reject the null hypothesis when it is true is equal to 13% and the probability that you will reject the null hypothesis when it is false is equal to 17%. The significance level of your test equals ________.
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A. B. C. D.D
The significance level equals the probability of making a Type I error, which is the error of rejecting the null when it is, in fact, true. In this case, this has been given to be equal to 13%.
To determine the significance level of the test, we need to understand the given probabilities and their relationship to the null hypothesis.
Let's define the probabilities mentioned in the question:
The significance level of a test, denoted as α (alpha), is the probability of rejecting the null hypothesis when it is actually true. In other words, it represents the probability of making a Type I error, which is the error of rejecting a true null hypothesis.
According to the question, P(Reject | True) = 13%, which means that when the null hypothesis is true, there is a 13% chance of rejecting it. This is the significance level (α) we are looking for.
Therefore, the correct answer is D. 13%.