Test coin fairness from 560 tails in 1000 flips
Company: Databricks
Role: Data Scientist
Category: Statistics & Math
Difficulty: hard
Interview Round: Technical Screen
You flip a coin n = 1000 times and observe 560 tails.
At significance level α = 0.05, test whether the coin is fair.
- State the null and alternative hypotheses.
- Show the test statistic and its distribution/approximation.
- Compute (or approximate) the p-value.
- State your conclusion.
Assume an i.i.d. Bernoulli model for tails with probability p.
Overview: This problem evaluates hypothesis testing for proportions—formulating null and alternative hypotheses, applying the binomial-to-normal approximation, and interpreting p-values; it belongs to Statistics & Math for Data Scientist roles and is pitched at an introductory/undergraduate applied statistics level.