Expert: Ahmed Salami - 10/22/2008

Question
A central university has a student population of 60,000. the university is interested in determining what proportion of them is in favor of a new graading system. determine a sample size with confidence level of 95 percentage that will show the true porportion of population in favor of the new system within plus and minus 0.02.

Answer
Hi Akanksha,
Applying the  general formula for a  confidence interval, the
confidence interval for a proportion is

p ± zσ

where p is the proportion in the sample, z depends on the level of
confidence desired, and σ is the standard error of a proportion.

σ = sqrt[p(1-p)/N]

Since we dont know how many are in favour of the new grading system,
we take p = 0.5 for our estimation of σ.

Also, we require that p ± zσ = p ± 0.02
zσ = 0.02

A z table can be used to determine that z for a 95% confidence
interval is 1.96
And so,
1.96σ = 0.02
σ = 0.01
sqrt[0.5(1 - 0.05)/N] = 0.01
sqrt[(0.5)(0.5)/N] = 0.01
0.5/sqrtN = 0.01
sqrtN = 0.5/0.01
sqrtN = 50
N = 2500

It took some time, didnt it? I'm sorry about that.
Regards.