Compare Two Coin Proportions
Company: Uber
Role: Data Scientist
Category: Statistics & Math
Difficulty: medium
Interview Round: Technical Screen
You are given results from two independent coin-toss experiments:
- Coin A was tossed 100 times and landed heads 40 times.
- Coin B was tossed 1,000 times and landed heads 600 times.
Determine whether the probability of heads is statistically different between the two coins.
In your answer, specify:
1. The null and alternative hypotheses.
2. The appropriate statistical test.
3. The test statistic and approximate p-value.
4. A 95% confidence interval for the difference in head probabilities.
5. Any assumptions or caveats, especially given the large difference in sample sizes.
Quick Answer: This question evaluates proficiency in statistical inference for proportions, including hypothesis formulation, comparison of two independent samples, confidence interval interpretation, and interpretation of p-values and sampling variability.