Do you have ESP? A researcher looking for evidence of extrasensory perception (ESP) tests $500$subjects. Four of these subjects do significantly better $\left(P<0.01\right)$than random guessing.

(a) Is it proper to conclude that these four people have ESP? Explain your answer.

(b) What should the researcher now do to test whether any of these four subjects have ESP?

Given in the question that,

Number of subjects$=400$

Number of people that have ESP$=4$we have to find is it proper to conclude that these four people have ESP

Using the significance level, it is expected that at least $500\left(0.01\right)=5$of the total $500$individuals that could do significantly better if random guessing is done. It shows that there are more than $4$people that have ESP that could be used for random guessing.

therefore, it is not proper to conclude that these four people have ESP.

Given in the question that A researcher looking for evidence of extrasensory perception (ESP) tests $500$subjects. Four of these subjects do significantly better $\left(P<0.01\right)$than random guessing. We have to find out that what should the researcher now do to test whether any of these four subjects have ESP.

The researcher could ask the four people that have ESP to repeat the procedure and check if they are performing better or not. If any of the individual does better then he must be having ESP for random guessing.