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I've been reviewing the results of an interesting chemistry experiment a colleague of mine was conducting, and she sought some help analyzing the results. Would you be able to help, please?

The experiment settings

  • A set of 1,200 known chemical substances denoted $s_1, s_2, s_3, ..., s_{1200}$. 10 of which are have a specific feature (for example, carcinogenic), and the other 1190 lack this feature.
  • A sensor we would like to test. The sensor returns a list of 7 substance ids suspected to be carcinogenic; it should perform significantly better than choosing at random.

Results

From that list of 7 ids returned from the seonsor, 2 were actually carcinogenic, and 5 were not.

Analysis

I would like to know is the probability of finding exactly 2, or at least 2, carcinogenic substances out of the sample, and the P-Value of the result.

My best guess so far is a Hypergeometric Distribution. In other words,

$P\left(X=k\right) = {{{D \choose k} {{N-D} \choose {n-k}}}\over {N \choose n}}$, Where $n=7, N=1200, D=10, k=2$.

I am not sure how to calculate $P\left(X\geq k\right)$.

My question

What is the relevant probability distribution and P-Value for analyzing the results of such experiment?

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I think that you would use the Hypergeometric Distribution just calculate $(P = k)$ for $k = 2, 3,....7$ and then sum the results to get $P(X \geq k)$ the probability that X is greater than or equal to k.

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