A researcher is interested in whether people have psychic abilities (ESP). He conducts an ESP experiment in which a person guesses which of 4 cards the researcher has randomly picked. This process of guessing which of the 4 cards the researcher has randomly picked is repeated for 200 trials. If the person is just guessing, that is, they do not have ESP then they will guess the correct card about 25% of the time. If a person had ESP they should pick the correct card more often. The null hypothesis is that the person is guessing at random, while the alternative hypothesis is that the person has ESP. The significance level is 0.05.
One person who was tested for ESP got 69 correct answers. The P-value was 0.002. Which of the following describes the probability represented by the P-value for this test?
A.
The probability of 69 or more correct guesses if the person has ESP
B.
The probability of 69 or more correct guesses if the person does not have ESP
C.
The probability that the person does not have ESP if the person actually has ESP
D.
The probability that the person has ESP if the person actually does not have ESP
A. The probability of 69 or more correct guesses if the person has ESP
A. The probability of 69 or more correct guesses if the person has ESP
The correct answer is A. The probability of 69 or more correct guesses if the person has ESP.
A p-value represents the probability of obtaining a test statistic as extreme as, or more extreme than, the observed value, assuming that the null hypothesis is true. In this case, the null hypothesis is that the person is guessing at random, meaning they do not have ESP.
Since the person got 69 correct answers, the p-value represents the probability of observing 69 or more correct guesses if the person truly has ESP. This means that if the person were actually guessing at random, it would be very unlikely for them to achieve such a result.
It's important to note that a low p-value does not provide evidence for the alternative hypothesis (that the person has ESP). It simply suggests that the observed result is unlikely to occur if the null hypothesis is true. To draw a conclusion about the presence of ESP, additional evidence and analysis would be needed.