Question about sampling which I THINK relates to Bayesian reasoning.

liamcottam

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Sep 5, 2019
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I'm in over my head with this one...
  • 47,635 experiments are conducted.
  • The experiment can have two outcomes “convert” and “doesn’t convert”
  • 3.07% of experiments have the outcome ‘convert.’(The baseline?)
  • A sample of 2,143 is chosen at random from the experiment results.
  • What is the probability that the number of “converts” in the random sample is >6.4%
 
I'd say you can just use a binomial distribution. You know the exact population, since you are taking the sample from the existing results.
 
They want you to use the normal approximation to the binomial pdf.
\(\displaystyle n=47635,~p=Pr[\text{convert}] = 0.0307\)

\(\displaystyle \mu_p= n p,~\sigma_p = \sqrt{n p(1-p)}\)

That becomes the approximate distribution model of the population.
Then you sample that that with \(\displaystyle N_s = 2143,~\mu_s=\mu_p,~\sigma_s = \dfrac{\sigma_p}{\sqrt{N_s}}\)

That should get you enough to complete the problem.
 
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