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.  Using the sign test, what is the two-tailed p-value for this outcome?  

Answer 1

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Answer:

H0: p = 0.5

H1: p 0.5

We have p = 0.5

phat = 4/16 = 0.25 ( 4 tails out of 16 outcomes)

Std dev = sqrt(0.5*0.5/16) = 0.125

For two tailed test we have z = (phat - p)/SD

z = (0.25 - 0.5)/0.125 = -2

We get two tailed p value as 0.0455

which is lesser than 0.05

Hence we reject the null hypothesis and conclude that the coin is biased