Question 930088
We use the formula n = p(1-p)(z/E)^2 where


n = min sample size
p = sample proportion
z = critical number from the standard normal distribution
E = margin of error


In this case,


p = 0.16  (sample proportion)
z = 1.64485362695147  (based on the 90% confidence interval)
E = 0.02 (Margin of error)



Note: I used a calculator to compute z. You can use a table to find z.



Let's plug those values into the formula and solve for n



n = p(1-p)(z/E)^2


n = 0.16(1-0.16)(1.64485362695147/0.02)^2


n = 909.062600576059 ... use a calculator here


n = 910 ... Always round UP (to the nearest whole number)



Why do we round up? If we rounded down, then we would come up short and the margin of error would be too big. If we used n = 909, then the margin of error would exceed E = 0.02. If we use n = 910, then E would be less than 0.02 as desired.



So the min sample size required is <font size=5 color="red">910</font>


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