Question 1201283
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Answer: <font color=red>16052</font>



Explanation:


At 99% confidence, the z critical value is roughly z = 2.576 
Use a table like this
<a href = "https://www.sjsu.edu/faculty/gerstman/StatPrimer/t-table.pdf">https://www.sjsu.edu/faculty/gerstman/StatPrimer/t-table.pdf</a>
to get that value. Look at the bottom row labeled "Z" and above the 99% confidence level.
A stats calculator can also compute this value.


We want the error level (E) to be 0.01
E = 0.01
This is to represent being within 1% of the target.


The value of phat (sample proportion) is
phat = 118/200
phat = 0.59
which indicates 59% of the sample students receive financial aid.
phat's job is to estimate the population proportion p.


Here is the summary of input values
z = 2.576 (approximate)
phat = 0.59
E = 0.01


Let's compute the minimum sample size needed.
n = phat*(1-phat)*(z/E)^2
n = 0.59*(1-0.59)*(2.576/0.01)^2
n = 16051.942144  approximately
n = <font color=red>16052</font>  always round UP to the nearest whole number



Further Reading:
<a href = "https://www.ltcconline.net/greenl/courses/201/estimation/ciprop.htm">https://www.ltcconline.net/greenl/courses/201/estimation/ciprop.htm</a>
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