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Lumifer comments on Open thread, July 28 - August 3, 2014 - Less Wrong Discussion

5 Post author: polymathwannabe 28 July 2014 08:27PM

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Comment author: Coscott 29 July 2014 07:52:12AM 4 points [-]

For a quick reminder of the power of many independent trials, estimate and then answer the following question:

I have 2 biased coins in my pocket. The first comes up heads with probability 51%, while the second comes up heads with probability 49%. I take a coin out of my pocket, uniformly at random, and flip it a million times. I observe that it comes up heads 508,634 times. What is the probability that it is the first coin?

Comment author: Lumifer 31 July 2014 07:53:35PM *  3 points [-]

Under the usual convention of 95% significance, it's neither :-D

 > binom.test(508634, 1000000, 0.51) Exact binomial test
data: 508634 and 1e+06
number of successes = 508634, number of trials = 1e+06, p-value = 0.006304
alternative hypothesis: true probability of success is not equal to 0.51
95 percent confidence interval:
0.5077 0.5096
sample estimates:
probability of success 0.5086
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