Compare Two Coin Proportions

You have results from two separate coin-flip experiments:

• Coin A was flipped 100 times and came up heads 40 times.
• Coin B was flipped 1,000 times and came up heads 600 times. Assess whether the probability of heads differs statistically between the two coins. Your answer should state:

1. The null and alternative hypotheses.
2. The appropriate statistical test.
3. The test statistic and an approximate p-value.
4. A 95% confidence interval for the difference in head probabilities.
5. Any assumptions or caveats, particularly because the sample sizes differ greatly. Overview: This problem tests skill in statistical inference for proportions, covering hypothesis formulation, comparison of two independent samples, confidence interval interpretation, and understanding of p-values and sampling variability.