SOLUTION: A university dean is interested in determining the proportion of students who receive some sort official aid. Rather than examine the records for all students, the dean randomly se

Question 1201283: A university dean is interested in determining the proportion of students who receive some sort official aid. Rather than examine the records for all students, the dean randomly selects 200students and finds that 118 of them are receiving financial aid. If the dean wanted to estimate the proportion of all students receiving financial aid to within1% with99% reliability, how many students would need to be sampled?
Answer by math_tutor2020(3816) (Show Source): You can put this solution on YOUR website!

Answer: 16052

Explanation:

At 99% confidence, the z critical value is roughly z = 2.576
Use a table like this
https://www.sjsu.edu/faculty/gerstman/StatPrimer/t-table.pdf
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 = 16052 always round UP to the nearest whole number

Further Reading:
https://www.ltcconline.net/greenl/courses/201/estimation/ciprop.htm

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