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Compare Two Coin Proportions

UberData Scientist · Technical Screen
MediumData ScientistTechnical ScreenStatistics & Math

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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.

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.