The null is straightforward, coin is fair so p=0.5.
State the null hypothesis that the coin is fair (p=0.5) and compute the p-value as the probability of observing 1 or fewer heads in 10 flips under the null. Use the binomial distribution to calculate the two-sided p-value, and briefly mention that this is a small sample so exact methods are appropriate.
Pro tip: Always clarify whether the test is one-sided or two-sided; in fairness testing, a two-sided test is standard, but Amazon interviewers may appreciate you noting that the alternative could be one-sided if you suspect bias in a specific direction.
Clearly state H0: the coin is fair, i.e., the probability of heads p = 0.5. Also mention the alternative hypothesis H1: p ≠ 0.5 (two-sided) or p < 0.5 (one-sided) depending on the context.
The number of heads in 10 flips follows a Binomial(10, 0.5) distribution under H0. The test statistic is the observed count of heads, which is 1.
For a two-sided test, calculate the probability of observing a result as extreme or more extreme than 1 head. This includes 0 heads and 1 head, and symmetrically 9 and 10 heads. Sum the binomial probabilities: P(X ≤ 1) + P(X ≥ 9) = 2 * (P(X=0) + P(X=1)) = 2 * (0.0009766 + 0.0097656) ≈ 0.0215.
The p-value is approximately 0.0215. At a significance level of 0.05, we reject the null hypothesis and conclude that there is evidence the coin is not fair. However, note that with only 10 flips, the test has low power.
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