Probability of Making a Type I Error

E

Alpha is the probability of committing a type I error. So 0.05 = 1/20.

The probability of making a Type I error, denoted as α (alpha), is the probability of rejecting a null hypothesis when it is actually true. In statistical hypothesis testing, the null hypothesis represents the default assumption, and the alternative hypothesis represents the claim we want to test.

In this question, the alpha level is given as 0.05, or 5%. It is a common convention to set the alpha level at 0.05 in many statistical tests. This means that we are willing to accept a 5% chance of making a Type I error.

Now, let's examine the answer choices:

A. None of these answers: This option implies that none of the other answer choices are correct.

B. 20/20: This answer suggests that the probability of making a Type I error is 20 out of 20, which is equivalent to 100%. However, since the alpha level is 0.05 (5%), this answer is incorrect.

C. 0: This answer suggests that the probability of making a Type I error is 0, meaning there is no chance of making a Type I error. However, since the alpha level is set at 0.05, this answer is incorrect.

D. 19/20: This answer implies that the probability of making a Type I error is 19 out of 20, or 95%. Since the alpha level is 0.05 (5%), this answer is incorrect.

E. 1/20: This answer suggests that the probability of making a Type I error is 1 out of 20, or 5%. This aligns with the given alpha level of 0.05, so this answer is correct.

Therefore, the correct answer is E. 1/20, as it represents the probability of making a Type I error when the alpha level is 0.05.