Question

One classical experiment in extrasensory perception tests the ability of an individual to show telepathy - to read the mind of another individual. This test uses five cards with different designs, all known to both participants. In a trial, the 'sender' sees a randomly chosen card and concentrates on the design. The 'receiver' attempts to guess the identity of the card. Each of the five cards is equally likely to be chosen, and only one card is the correct answer at any point

1. Which of the following is an appropriate null hypothesis for this telepathy experiment?

   		The proportion of correctly identified cards by the receiver is greater than 0.2
   		The proportion of correctly identified cards by the receiver is 0.2
   		The proportion of correctly identified cards by the receiver is something other than 0.2
   		The proportion of correctly identified cards by the receiver is less than 0.2

2. Which of the following is an appropriate alternative hypothesis for this telepathy experiment, if a two tailed test is to be used?

   		The proportion of correctly identified cards by the receiver is greater than 0.2
   		The proportion of correctly identified cards by the receiver is 0.2
   		The proportion of correctly identified cards by the receiver is something other than 0.2
   		The proportion of correctly identified cards by the receiver is less than 0.2

3. Which of the following is an appropriate alternative hypothesis for this telepathy experiment, if a one tailed test is to be used?

   		The proportion of correctly identified cards by the receiver is greater than 0.2
   		The proportion of correctly identified cards by the receiver is 0.2
   		The proportion of correctly identified cards by the receiver is something other than 0.2
   		The proportion of correctly identified cards by the receiver is less than 0.2

4. In this experiment we are really trying to see if mind reading occurs. That is we are trying to prove that the sender can actually tell telepathically the receiver what card he is seeing. True or false: In this context we should really use a one tailed test.

   True

   False

5. Out of 10 trials, a receiver got four cards correct. What is the probability of that particular outcome (4 correct guesses out of 10) if the receiver was guessing, that is picking the cards at random? Round off to THREE digits after the decimal point.

6. Out of 10 trials, a receiver got four cards correct. What is the probability of that particular outcome (4 correct guesses out of 10) if the receiver was guessing, that is picking the cards at random? Round off to THREE digits after the decimal point.

7. Out of 10 trials, a receiver got four cards correct. (This is identical to question 5). What is the P-value from a two tailed binomial test corresponding to this result? Round off to TWO digits after the decimal point. (Write down the answer, you will need it for the next questions.

   8) Out of 10 trials, a receiver got four cards correct. (This is identical to question 5). What is the lower bound of the Agresti-Coull confidence interval for the proportion of correctly identified cards? Round off to TWO digits after the decimal point.

   9) Out of 10 trials, a receiver got four cards correct. (This is identical to question 5). What is the upper bound of the Agresti-Coull confidence interval for the proportion of correctly identified cards? Round off to TWO digits after the decimal point.

   10) Based on the result from the one tailed binomial test do you reject the null hypothesis?

   11) Based on the result of the one tailed binomial test, which of the following is an appropriate conclusion from the observation of 4 correctly identified cards out of 10 trials?

Answer 1