Question : Trying to understand Excel formula for sample size, sat confidence level and probability

The attached file is a Sample Size calculator that I downloaded and I'm trying to understand how the formulas work.  I'm trying to understand some of the code in the formula on sample size.

This calculates the minimum sample size based on the confidence level (=NORMSINV(1-0.5*(1-E1)) and confidence interval (E2) and percentage (E3):

=ROUNDUP((($F$1^2*$E$3*(1-$E$3))/($E$2^2))/(1+(((((($F$1^2)*$E$3*(1-$E$3))/($E$2^2)))-1)/A2)),0)

Questions -- does "^2" mean $F$1is squared?
-- also, why does the minimum sample size only change from 191 for 1185 records to 224 for 12999 records?  Shouldn't the 12999 have a much bigger minimum sample?

Answer : Trying to understand Excel formula for sample size, sat confidence level and probability

Hello billb1057,

>> Questions -- does "^2" mean $F$1is squared?

Yes.  In Excel, ^ is the exponentiation operator.

>> -- also, why does the minimum sample size only change from 191 for 1185 records to 224 for 12999 records?  
>> Shouldn't the 12999 have a much bigger minimum sample?

Because the relationship between the required sample size and the total population is *not* linear.  As the
population grows, as long as your sample is truly random, you reach a point of diminishing returns in terms
of required sample sizes.

Please have a look at the comment I posted to this article: http://www.experts-exchange.com/articles/Internet/Web_Development/Marketing/Conducting-a-Survey.html

In it, I explain why the sample size requirements the author posted are correct.  To get the same results, ignoring
rounding, set your confidence level to 95%, confidence interval to 3%, and percentage to 50%.

Regards,

Patrick