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Extra Sensory Perception Test

In: Science

Submitted By luatagal
Words 820
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AP Stats
ESP Simulation

First Step:
a) What are we trying to find or solve?
We are trying to find out how well an ordinary non-ESP-endowed person may do by chance on matching 10 people to their signatures (contained in envelopes). We will then use this information to determine whether our friend is ESP-endowed by whether or not he is above average.
b) What do we already know? My friend claims he has “ESP”. I know that I will get ten volunteers to sign their names on identical cards and then seal them in identical envelopes. After shuffling the envelopes I’ll hand them to my friend to see if he will be able to distribute the envelopes back to the volunteers with the according signature.
Second Step:
a) Identify the component to be repeated. The component to be repeated is to simulate randomly matching people with their signature.
b) Explain how you will model the component’s outcome.
I will use the numbers 0 through 9 to represent the envelopes. Using a random number generator I will list out 10 random numbers in the order they were received. I’ll then count how many of the random numbers are still in their numerical place. For example, if 0 was the first random number and 9 was the last random number picked then that would be counted as two correct matches.
c) Explain how you will combine the components to model a trial. By using the numbers 0-9 to model the envelopes, I will use random number generator to simulate matching the envelopes to the volunteers. I will not count any numbers that are repeated because each number is representative of one specific envelope and cannot be given to two volunteers. After counting how many numbers are in their regular numerical place one trial is complete. After running 20 trials I will take the average number of people matched to their signatures by chance. Anything above this average will be considered “statistically significant”.
d) State clearly what the response variable is. The response variable is the number of volunteers correctly matched to their signatures by chance.
Third Step:
a) Run several trials (magic minimum is 20) Trial Number | | #envelopes correctly matched | 1 | 8,5,4,7,3,0,1,6,9,2 | 0 | 2 | 1,0,3,5,4,6,8,9,7,2 | 1 | 3 | 7,5,1,4,3,6,2,8,0,9 | 1 | 4 | 6,7,8,3,2,1,9,0,5,4 | 1 | 5 | 9,1,7,5,3,0,2,4,8,6 | 2 | 6 | 7,1,9,4,2,0,6,3,5,8 | 2 | 7 | 3,1,9,4,7,6,0,9,5,2 | 1 | 8 | 1,0,2,7,5,4,8,6,3,2 | 1 | 9 | 1,7,3,5,0,9,6,2,4,8 | 1 | 10 | 8 9 7 1 5 6 0 4 2 3 | 0 | 11 | 8 0 2 6 7 1 4 9 5 3 | 1 | 12 | 4 6 9 2 8 7 3 1 5 0 | 0 | 13 | 7 5 8 3 2 1 0 6 9 4 | 1 | 14 | 3 0 7 1 9 2 8 6 4 5 | 0 | 15 | 2 4 7 9 5 8 3 0 1 6 | 0 | 16 | 0 6 9 7 2 3 8 4 1 5 | 1 | 17 | 8 2 4 5 0 3 7 9 6 1 | 0 | 18 | 4 7 9 3 1 2 5 0 6 8 | 1 | 19 | 0 5 9 8 7 6 2 1 4 3 | 1 | 20 | 9 8 7 1 2 4 6 3 5 0 | 1 |

b) Collect and summarize the results of all the trials. The average number of envelopes correctly matched was .8 envelopes which I will round to 1 envelope for realistic purposes. The most occurring number of envelopes correctly matched was 1 with a count of 12. The next was 0 with a count of 6. There were 2 counts of two envelopes being correctly matched.

c) State your conclusion. The highest number of correctly matched envelopes during my trials was 2. This means that the average non-ESP-endowed person is likely to correctly match 2 envelopes or less to the volunteers suring this test. I will conclude that if my friend succeeds in correctly matching more than 2 envelopes to the volunteers, there is some type of extrasensory perception (no matter how slight) going on.
Fourth Step: Does your solution sound reasonable? How so? Yes, I believe my solution sounds reasonable because it’s difficult to match ten envelopes correctly to their perspective person. Each person has a one in ten chance of getting their envelope while each envelope has a one in ten chance of being given to its person. Statistically, without any extrasensory perception, the chances of randomly matching more than 2 envelopes correctly are slim.

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