Question about sampling which I THINK relates to Bayesian reasoning.

[liamcottam]

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%

 

[Dr.Peterson]

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.

 

[Romsek]

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.