Sample Size for a Desired Margin of Error

[eutas1]

Hello,
Please refer to the attachment - I can see why the formula can be simplified to n = 0.25(z / E)^2 because you get 0.25 if you make p-hat= 0.5 But I don't see how it simplifies to n = ( z / 2E)^2 ?? Why isn't the 2 a 4? Isn't 0.25 = 1/4?
Apologies, this is probably a stupid question and the answer is probably so simple....

 

[Harry_the_cat]

It would be 4 if it was outside the bracket being squared. But it is inside the bracket being squared, so it becomes a 2. 2^2=4.

 

[Dr.Peterson]

Hello,
Please refer to the attachment - I can see why the formula can be simplified to n = 0.25(z / E)^2 because you get 0.25 if you make p-hat= 0.5 But I don't see how it simplifies to n = ( z / 2E)^2 ?? Why isn't the 2 a 4? Isn't 0.25 = 1/4?
Apologies, this is probably a stupid question and the answer is probably so simple....

Filling in the steps: [math]n = 0.25\left(\frac{z}{E}\right)^2 = \frac{1}{4}\left(\frac{z}{E}\right)^2 = \left(\frac{1}{2}\right)^2\left(\frac{z}{E}\right)^2 = \left(\frac{1}{2}\frac{z}{E}\right)^2 = \left(\frac{z}{2E}\right)^2[/math]

 

[eutas1]

It would be 4 if it was outside the bracket being squared. But it is inside the bracket being squared, so it becomes a 2. 2^2=4.

The 0.25 IS outside the bracket being squared......??

 

[eutas1]

Filling in the steps: [math]n = 0.25\left(\frac{z}{E}\right)^2 = \frac{1}{4}\left(\frac{z}{E}\right)^2 = \left(\frac{1}{2}\right)^2\left(\frac{z}{E}\right)^2 = \left(\frac{1}{2}\frac{z}{E}\right)^2 = \left(\frac{z}{2E}\right)^2[/math]

Ohhh I see I see. I didn't see that 1/4 can be changed to (1/2)^2
Thank you!