Question

What are the chances of seeing 11 or more heads in a trial of 15 unbiased coin throws? Would you reject the hypothesis that the coin is unbiased if you see 11 heads in 15 throws

Answer 1

If we would tesis that coin is equal from both sides than P(head)= P(not head)=1/2

P(11 heads out of 15)=cuz binomial distribution=C_{15}^{11}1/2^{11}*1/2^{4}=(1/2)^{15}*\frac{15+14+13+12}{4+3+2}=1365/2^{15}=4%

Would you reject the hypothesis that the coin is unbiased if you see 11 heads in 15 throws?

I think that could happen, so coin might be as unbiased and biased either.