How many consecutive tails would you need to establish that a coin is biased ($P_{heads} < 0.5$)
Null: $P_{heads} = p = 0.5$
So need $(1-p)^n < 0.05$ to establish bias at 95% confidence one sided
$\implies 0.5^n < 0.05$
$\implies n > \frac{\log(0.05)} {\log(0.5)}$
$\implies n \ge 5$
So it seems like we only need 5 tails to conclude that coin is biased?? That seems very low. Is there something I'm missing?