Is My Coin Toss Hypothesis Correct?

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If I hypothesize that 70% of all my future coin tosses will come up heads, and I sample 15 coin tosses and get 13 heads, what is the probability that my hypothesis is correct?
 

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Obviously you underestimated, so you need to calculate whether the difference 13/15 - 0.7 is significantly different from zero.

See figure 1 of http://www.sportsmed.org/tabs/research/downloads/Research%208%20-%20Discrete%20Data.pdf
 
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