Question

Suppose you and your roommate use a coin-flipping app to decide who has to take out the trash: heads you take out the trash, tails your roommate does. After losing a number of flips, you start to wonder if the coin-flipping app really is totally random, or if it is biased in one direction or the other.

To be fair to your roommate, you wish to test whether the app is biased in either direction, and thus a two-tailed test is appropriate. You borrow your roommate's phone long enough to flip the virtual coin 16 times and you get 12 heads and 4 tails.  

To test the two-tailed null hypothesis, you will have to look at the probabiltie(s) of which possible outcomes?

Answer 1

H0: Null Hypothesis: p = 0.5 ( the coin-flipping app really is totally random )

HA: Alternative Hypothesis: p 0.5 ( the coin-flipping app is biased in one direction or the other. )

Answer is:

To test the two-tailed null hypothesis, you will have to look at the probabilty of difference between observed proportion : = 12/16 = 0.75 and the hypothesized proportion = p0 = 0.5 is small enough to attribute to only statistical variation and not due to attributable causes.