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I thought the first part of the question was very straightforward. Calculating the p-value of 56/1024 was easy. But Google was very interested in how you analyzed it. I was asked what else I could do to test the fairness of thecoin. To answer it, I mentioned chi-squared distribution and its test statistic. Then Google guy asked me that "is this an approximation?" He went on and asked me "if I tossed the coin more than 10 times, say 100 times, would it help?"
- midtownguru November 04, 2013For the second part of the question, I had to pause for about five seconds before I opened my mouth. I though I needed to modify it because if you stick to 5% significant level for each coin, then the probability for failing to detect a biased coin would decrease for 10 coin case. I mean 0.95^10 = 0.6. So you could fail to find a biased coin 4 our of 10. In order to be 95% sure, you need to raise the significance level to 0.05/10 = 0.5% for each coin. I think this is similar to Bonferroni confidence band.
I don't know the answer. Gooogle didn't give me any answer during the interview.