FDS Week 22 Quiz

A magician claims that he can read your mind. In a binary game where you have to choose 0 or 1, the magician has to read your mind and guess which one you chose. If he gets it right you win, else he wins.

In this case, the solution says p = 0.5. How is this so? This tells that for the magician to win, he has to be right only about 50% of the time. Should he not be correct all the time?

if he gets it right, he wins (not you win).

For Null Hypothesis, we consider the ordinary (basically what is obvious/easy) and then try to reject or accept it. Now, if somebody guesses in a binary game (right or wrong), whats the ordinary, obvious chance of winning: 50%, Right? Hence p=0.5.

Now, if somebody makes a guess 6 times, it doesn’t necessary mean that he will be right exactly 3 times. But if you keep playing this guessing game again and agin, it will average out to be 50%. (Note: This means, if you look at ONLY one set of 6 guesses, sometime it will be correct 3 times, sometime MORE and sometime LESS. Key is average)

In this particular example, the magician guesses 4 times correctly out of 6. That is he correctly guessed more than 50% of the time (66.67%).
Does this give us sufficient confidence to say yes the magician can guess(read) our mind?
Does this mean the Alternate Hypostheis (that he is right more than 50%) is correct?

Week 22 videos show us how to calculate this confidence? It shows how far we have to be from the Null Hypothesis to reject it? So the question is if guessing correctly 4/6 is far enough from 3/6 (null hypothesis) that we can say with high confidence he can read the mind.

Magician claims he can read our mind. So he has to consistently guess (much) more than 50% (not just one time) to convince that he can actually read the mind.

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