# sample size

• Nov 25th 2011, 03:29 AM
bubblygirl90
sample size
i have a formula for the sample size as
n=A * [ ( (a+t)(1-a-t) + a(1-a) ) / t^2 ], where A, a & t are all unknown constants.
The question is to show that n has a maximum when
a = (1-t)/2

I think the A can just be ignored so that I need to find the maximum of the top line and minimum of the bottom. Since the bottom is just t^2 and fixed I can't do anything with it so just need to maximise the top?
At first I differentiated the top with respect to t and ended up with a = (1-2t)/2, although since t is constant I don't think I can do this?

Any help would be very welcome!
• Nov 25th 2011, 03:33 AM
alexmahone
Re: sample size
Quote:

Originally Posted by bubblygirl90
i have a formula for the sample size as
n=A * [ ( (a+t)(1-a-t) + a(1-a) ) / t^2 ], where A, a & t are all unknown constants.
The question is to show that n has a maximum when
a = (1-t)/2

I think the A can just be ignored so that I need to find the maximum of the top line and minimum of the bottom. Since the bottom is just t^2 and fixed I can't do anything with it so just need to maximise the top?
At first I differentiated the top with respect to t and ended up with a = (1-2t)/2, although since t is constant I don't think I can do this?

Any help would be very welcome!

You need to differentiate the top with respect to a.
• Nov 25th 2011, 03:48 AM
bubblygirl90
Re: sample size
Quote:

Originally Posted by alexmahone
You need to differentiate the top with respect to a.

Ahh, so simple! Don't know why i didn't see that (Giggle)

Thank you!