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I need a bit of clarification to understand sampling distributions through Khan Academy. My answer is widely different than the answers given in the sample The example question can be summarized as:

Of a population of 1750 students, 15% have reported extreme levels of stress that month. A school newspaper does not know this figure and carries out survey to determine what it is. A simple random sample of 160 students were asked if they experienced extreme levels of stress that month...10% of the sample replied "yes" to the question.

Assuming the true proportion is 15%, what is the approximate probability that more then 10% of the sample would report that they experience extreme levels of stress during the past month?

Answer: P(p>0.1)=0.96

My attempted answer is: $$\mu_{\hat{p}}=\hat{p}=0.10$$ $$\sigma_{\hat{p}}=sqrt((0.1*0.9)/160)=0.0237$$ Using these values, my cumulative probability of $P(p>10)\approx 0.50%$.

The example video uses $\mu_{\hat{p}}=p_{pop}=0.15$ but I fail to understand why because the question explicitly states that they do not know the true population parameter. Please help me clarify my understanding

video reference on KA

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    $\begingroup$ This does not seem to be a matter of statistical inquiry, but merely one of careful analysis of the English text. The question explicitly states the "true proportion" (which thereby refers to the entire population) is 15%: nowhere does it state or imply this value is unknown. It does ask about a property of samples from this population, samples which vary randomly. $\endgroup$ – whuber Dec 28 '18 at 23:38
  • $\begingroup$ Can you please add the self-study tag? $\endgroup$ – kjetil b halvorsen Dec 31 '18 at 12:17

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