21. One classical experiment on ESP (extrasensony perception) tests for the abil

Question

21. One classical experiment on ESP (extrasensony perception) tests for the ability of an individual to show telepathy-to read the mind of another individual. This test uses five cards with differ- ent designs, all known to both participants. Ina trial, the "sender" sees a randomly chosen card and concentrates on its 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. a. Out of 10 trials, a receiver got four cards correct. What is her success rate? Wha only gnected rate of success, assuming she her expected rate of success, assuming t is only guessing? assuming sheis 15.html.

Explanation / Answer

a)

Here success rate is

p^ = 4/10 = 0.4 [ANSWER]

If she was guessing, her expected rate is,

p = 1/5 = 0.2 [ANSWER]

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B)

Ho: p <= 0.2
Ha: p > 0.2

Note that P(at least x) = 1 - P(at most x - 1).          
          
Using a cumulative binomial distribution table or technology, matching          
          
n = number of trials =    10      
p = the probability of a success =    0.2      
x = our critical value of successes =    4      
          
Then the cumulative probability of P(at most x - 1) from a table/technology is          
          
P(at most   3   ) =    0.879126118
          
Thus, the probability of at least   4   successes is  
          
P(at least   4   ) =    0.120873882

As this is not a small P value, we fail to reject Ho.

This is NOT RELIABLE EVIDENCE that the receiver has telephatic abilities.

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c)

For larger sample sizes, the variation in sample proportion becomes smaller, hence, it is harder to produce a sample proportion far from the population proportion. Hence, this becomes significant (due to large sample size) even though it is a lower sample proportion.

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