# Suppose a single card is held up and the subject is just guessing when responding

1. Suppose a single card is held up and the subject is just guessing when responding as to which shape is on the card. What is the probability that the subject will guess correctly? 2. If a subject is just guessing the shape on a card at random, what proportion (out of 25 cards) would you expect the person to correctly identify? 3. Look again at your answer to Question 2. How would you expect that proportion to change if someone actually does have ESP (assuming that ESP exists)? In other words, would you expect the proportion to be larger or smaller than what you wrote down in response to Question 2? Think carefully about what is going on here. We have two competing hypotheses. It could be that an individual is just guessing when trying to identify the symbol on the card, or, it could be that the individual has psychic abilities (or ESP) and is not just guessing. How can we rule out that a person is just guessing? Think about that as we move forward in this activity. 4. How might we determine whether an observed result is “extreme” enough to suggest someone might truly have ESP? Statisticians do this by employing a p-value. This is the probability of obtaining a sample statistic as extreme or more extreme than the observed sample statistic, if we assume to begin with that our null hypothesis is true. A. In this example, we start with a hypothesis that subjects are just guessing when presented with Zener cards and would do no better than what is expected “just by chance alone.” We would write this hypothesis out as follows: Ho: p = 0.20. We call this the __________________ hypothesis. B. Remember that with hypothesis testing, we always begin with a set of competing hypotheses. This means we must have another hypothesis that subjects do indeed have psychic powers and thus would do better than “just guessing.” In symbols, we would write this hypothesis as: Ha: p > 0.20. We call this the ______________________hypothesis.