Outcomes and the Type I and Type II Errors Quiz

PDF page 496: When you perform a hypothesis test, there are four possible outcomes depending on the actual truth, or falseness, of the null hypothesis H0 and the decision to reject or not. The outcomes are summarized in the following table:

PDF page 496: When you perform a hypothesis test, there are four possible outcomes depending on the actual truth, or falseness, of the null hypothesis H0 and the decision to reject or not. The outcomes are summarized in the following table:

PDF page 496: Each of the errors occurs with a particular probability. The Greek letters α and β represent the probabilities. α = probability of a Type I error = P(Type I error) = probability of rejecting the null hypothesis when the null hypothesis is true.

PDF page 496: β = probability of a Type II error = P(Type II error) = probability of not rejecting the null hypothesis when the null

PDF page 496: Each of the errors occurs with a particular probability. The Greek letters α and β represent the probabilities. α = probability of a Type I error = P(Type I error) = probability of rejecting the null hypothesis when the null hypothesis is true.

PDF page 496: hypothesis is false. α and β should be as small as possible because they are probabilities of errors. They are rarely zero. The Power of the Test is 1 – β. Ideally, we want a high power that is as close to one as possible. Increasing the sample size can increase the Power of the Test. The following are examples of Type I and Type II errors.

PDF page 496: hypothesis is false. α and β should be as small as possible because they are probabilities of errors. They are rarely zero. The Power of the Test is 1 – β. Ideally, we want a high power that is as close to one as possible. Increasing the sample size can increase the Power of the Test. The following are examples of Type I and Type II errors.

PDF page 496: hypothesis is false. α and β should be as small as possible because they are probabilities of errors. They are rarely zero. The Power of the Test is 1 – β. Ideally, we want a high power that is as close to one as possible. Increasing the sample size can increase the Power of the Test. The following are examples of Type I and Type II errors.

PDF page 496: hypothesis is false. α and β should be as small as possible because they are probabilities of errors. They are rarely zero. The Power of the Test is 1 – β. Ideally, we want a high power that is as close to one as possible. Increasing the sample size can increase the Power of the Test. The following are examples of Type I and Type II errors.

PDF page 497: Type II error: Frank goes climbing, thinking that his equipment is safe, but this is a mistake, and he painfully realizes that his equipment is not as safe as it should have been. Frank assumed that the null hypothesis was true, when it was not. α = probability that Frank thinks his rock climbing equipment may not be safe when, in fact, it really is safe. β = probability that Frank thinks his rock climbing equipment may be safe when, in fact, it is not safe. Notice that, in this case, the error with the greater consequence is the Type II error. (If Frank thinks his rock climbing equipment is safe, he will go ahead and use it.)

PDF page 497: Suppose the null hypothesis, H0, is: a tomato plant is alive when a class visits the school garden. Type I error: The null hypothesis claims that the tomato plant is alive, and it is true, but the students make the mistake of thinking that the plant is already dead. Type II error: The tomato plant is already dead (the null hypothesis is false), but the students do not notice it, and believe that the tomato plant is alive. α = probability that the class thinks the tomato plant is dead when, in fact, it is alive = P(Type I error). β = probability that the class thinks the tomato plant is alive when, in fact, it is dead = P(Type II error). The error with the greater consequence is the Type I error. (If the class thinks the plant is dead, they will not water it.)

PDF page 497: Type II error: Frank goes climbing, thinking that his equipment is safe, but this is a mistake, and he painfully realizes that his equipment is not as safe as it should have been. Frank assumed that the null hypothesis was true, when it was not. α = probability that Frank thinks his rock climbing equipment may not be safe when, in fact, it really is safe. β = probability that Frank thinks his rock climbing equipment may be safe when, in fact, it is not safe. Notice that, in this case, the error with the greater consequence is the Type II error. (If Frank thinks his rock climbing equipment is safe, he will go ahead and use it.)

PDF page 496: Suppose the null hypothesis, H0, is: Frank's rock climbing equipment is safe. Type I error: Frank does not go rock climbing because he considers that the equipment is not safe, when in fact, the equipment is really safe. Frank is making the mistake of rejecting the null hypothesis, when the equipment is actually safe!