An ESP experiment is done in which a participant guesses which of 8 cards the researcher has randomly picked, where each card is equally likely to be selected. This is repeated for 200 trials. The null hypothesis is that the subject is guessing, while the alternative is that the subject has ESP and can guess at higher than the chance rate. Write out the type 1 and type 2 errors in terms of this problem.
MY ANSWER IS TYPE 1 -- ?????
In hypothesis testing, a Type I error refers to rejecting the null hypothesis when it is actually true. In this specific scenario, the null hypothesis is that the participant is guessing, while the alternative hypothesis is that the participant has ESP and can guess at a rate higher than chance.
So, in terms of this problem:
Type I error: Rejecting the null hypothesis (i.e., concluding that the participant has ESP) when, in reality, the participant is just guessing and there is no actual ESP ability. Essentially, this would mean concluding that there is a true positive effect (ESP) when one does not exist.
Type II error: Failing to reject the null hypothesis (i.e., concluding that the participant is just guessing) when, in reality, the participant does have ESP and can guess at a rate higher than chance. In other words, this would mean failing to detect a true positive effect (ESP).
To summarize:
Type I error: Concluding that the participant has ESP when they are actually just guessing.
Type II error: Failing to conclude that the participant has ESP when they actually do have ESP.