A Lopsided Coin and Its Two Tails
A coin is claimed to land heads with probability 1/3. It is tossed 8 times and lands heads 6 times. Use the exact binomial test of $H_0: p = 1/3$ with the two-sided p-value defined as the total probability, under $H_0$, of all outcomes whose probability is **at most** the probability of the observed outcome (the convention used by R's `binom.test`; it is not "double the smaller tail"). Give the p-value as a reduced fraction.
Related problems & prerequisites
Worth solving first
- Power of a Ten-Flip Test 2.0/10
- Seven of Eight Recovered 2.0/10
- Power of a One-Sided Uniform Test 2.0/10
Source: Original problem written for AxiomIQ.