Question

A study conducted by researchers at Penn State investigated whether time perception is impaired during alcohol withdrawal. They hypothesized that people with withdrawal symptoms overestimate the elapsed time. After 24 hours of alcohol abstinence, 20 alcoholics were asked to estimate how much time had passed during a 45-second period, revealed an average time of 59.3 seconds with a standard deviation of 9.83 seconds. Explain the meaning of Type 1 and 2 errors and Power in the context of the problem.

Answer 1

In the context of the problem, Type 1 error refers to the rejection of the null hypothesis when it is actually true. Type 2 error refers to the failure to reject the null hypothesis when it is actually false. Power refers to the probability of correctly rejecting the null hypothesis when it is false.

Step-by-step explanation:

In the context of the problem, Type 1 error refers to the rejection of the null hypothesis when it is actually true. In this case, it would mean concluding that people with withdrawal symptoms overestimate the elapsed time, when in fact they do not.

Type 2 error, on the other hand, refers to the failure to reject the null hypothesis when it is actually false. In this case, it would mean concluding that people with withdrawal symptoms do not overestimate the elapsed time, when in fact they do.

Power, in the context of this problem, refers to the probability of correctly rejecting the null hypothesis when it is false. It is the complement of the Type 2 error rate.

A high power indicates a higher likelihood of detecting a true effect. In this study, a high power would indicate a higher likelihood of correctly concluding that people with withdrawal symptoms overestimate the elapsed time.