Question 1202810
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At 95% confidence, the critical z value is roughly z = 1.960. Use a table or stats calculator to determine this. 


E = margin of error 
E = 0.035
This is the decimal form of 3.5%


phat = sample proportion
phat's job is to estimate the population proportion (p).
Since we do not know the value of phat, we go with the most conservative estimate of phat = 0.5 which is right in the middle between 0 and 1.



Here are the values we'll plug in
z = 1.960
E = 0.035
phat = 0.5


Plug them into the formula below
n = phat*(1-phat)*(z/E)^2
n = 0.5*(1-0.5)*(1.96/0.035)^2
n = 784 


In this case we landed exactly on 784 without needing to round. 
In most cases we'll get some decimal value. 
The idea is to round UP to the nearest integer. Always round up. 
This is to clear the hurdle needed.



Answer: 784


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Extra info:


You may be wondering "where did that formula come from?"


It's the result of solving
E = z*sqrt(phat*(1-phat)/n)
for the variable n. 
This second formula computes the margin of error for a confidence interval proportion.


Let's solve for n.
E = z*sqrt(phat*(1-phat)/n)
E/z = sqrt(phat*(1-phat)/n)
(E/z)^2 = phat*(1-phat)/n
(z/E)^2 = n/( phat*(1-phat) )
phat*(1-phat)*(z/E)^2 = n
n = phat*(1-phat)*(z/E)^2
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