## midtownguru

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AnswersTossing a coin ten times resulted in 8 heads and 2 tails. How would you analyze whether a coin is fair? What is the p-value?

- midtownguru in United States

In addition, more coins are added to this experiment. Now you have 10 coins. You toss each coin 10 times (100 tosses in total) and observe results. Would you modify your approach to the the way you test the fairness of coins?| Report Duplicate | Flag | PURGE

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Yes. This team does some machine learning in Google. They are called quantitative analysts or statistician engineers. They work on projects to improve search engine and ads.

- midtownguru November 04, 2013Page:

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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.