Test coin fairness from 560 tails in 1000 flips

A coin is tossed $n = 1000$ times, yielding 560 tails.

With a significance level of $\alpha = 0.05$, test whether the coin is fair.

• Write down the null and alternative hypotheses.
• Provide the test statistic along with its distribution or approximation.
• Calculate or estimate the p-value.
• Give your conclusion.

Take the tails to follow an i.i.d. Bernoulli model with probability $p$.

Overview: This question checks your grasp of proportion hypothesis testing: writing null and alternative hypotheses, invoking the normal approximation to the binomial, and reading p-values. It is categorized under Statistics & Math for Data Scientist roles and sits at an introductory/undergraduate applied statistics difficulty.