Question

Which of the following statements is true?

a. The probability of committing a Type II error is the represented by the Greek letter α.

b. The probability of committing a Type II error is the same as the level of significance.

c. The probabilities of committing Type I and Type II errors are related such that when one is increased, the other will increase also.

d. The probability of committing a Type I error is the represented by the Greek letter β.

e. The decision maker controls the probability of committing a Type I error.

Answer 1

Answer:

Step-by-step explanation:

Hello!

When making a hypothesis test you can make two decisions "to reject· and "to not reject" the null hypothesis.

There are also two possibilities regarding the null hypothesis, that it is "true" or it is "false"

So there are possible cases:

• To reject the null hypothesis and the null hypothesis is false. In this case, the decision is CORRECT.⇒ Its associated probability is symbolized 1 - β and is known as the power of the test.
• To reject the null hypothesis but the null hypothesis was true. In this case, you've made a Type I error.⇒ Its associated probability is α, known as the signification level.
• To not reject the null hypothesis, the null hypothesis is true. This decision is CORRECT. ⇒ Its associated probability is symbolized as 1 - α
• To not reject the null hypothesis, the null hypothesis is false. In this case, the error made is a Type II error. ⇒ Its associated probability is symbolized β

Keeping this in mind,

a. The probability of committing a Type II error is represented by the Greek letter α.

FALSE, it is symbolized by β

b. The probability of committing a Type II error is the same as the level of significance.

FALSE, the Type II error is when you don't reject the null hypothesis and this is false. The level of significance is the probability of committing a Type I error.

c. The probabilities of committing Type I and Type II errors are related such that when one is increased, the other will increase also.

CORRECT, check graphic, alpha is the probability of rejecting the null hypothesis when it is true because it is a case where the hypothesis is true, that is why it is marked under the curve corresponding to the null hypothesis.

The Type II error is not rejecting the null hypothesis when it is false. Since the hypothesis is false, then the alternative is true, therefore its associated probability is marked under the curve that corresponds to the alternative hypothesis.

Remember hypotheses are complementary and exhaustive (this means that between them are include all possible outcomes that the experiment can take.) So graphically, every possibility is contained under the curve of the null hypothesis or the curve of the alternative hypothesis.

So, in the sense of the direction of the hypothesis (in the example how the curve of the alternative hypothesis is on the right, then the hypothesis is unilateral right) in the conjunction of the "arms" of many curves, you can find yourself in the situation of committing type one error or type two error (depending on the statistic value). So looking at it from the painted areas under the curve when you increase the area of α decreases the are of β and if you decrease the area of ​​α then the area of ​​β increases.

d. The probability of committing a Type I error is represented by the Greek letter β.

FALSE, the Type I error is symbolized by α.

e. The decision-maker controls the probability of committing a Type I error.

CORRECTt, the signification level is chosen by the investigator.

I hope it helps!