Extra Sensory Perception (ESP) is a controversial ability where some people claim to be able to see things or make predictions about future events. Whether or not the existence of ESP is part of one's beliefs, the concept does pose a question that can and has been studied and analyzed using the same statistical methods you will be learning in this class.

The classic study involved volunteers whose psychic abilities were tested using five cards with each with a different shape. We will use a standard deck of playing cards differentiating the particular card by suit. Take a deck of cards and select four cards each with a different suit, find a willing partner, and use these cards to test each other's psychic ability.

Part 1

1. The StatisticalHypothesis.

Write down the appropriate statistical hypothesis for deciding whether or not a particular subject might have ESP. Think about what the theory would be and what the status quo opinion would be.

H₀:

H₁:

2. The variable.

Let x= the number of correct guess out of ten attempts.

Write down the sample space (the set of all possible values) of this variable.

{ }

3. Conducting thesimulation.

Using the four playing cards you have acquired, testeach other a few times. In other words, give each other ten attempts and record the number of correct guesses for each set of ten tries. Use the table below to record your results. The more iterations of the experiment you do, the better you will see the approximate distribution with your frequency plot inpart4.

4. Draw a frequency plot of the results from part3.

5. Describe the shape of the distribution indicated by the frequency plot in part4.

6. Given the Statistical hypothesis in part 1 and the approximate distribution in part 4, give a decision rule and estimate the type I error rate using the approximate distribution in part4.