When I plug numbers into the equation I get .0184… Why do we divide our old margin of error by the sqrt of 4 instead of just using the full equation?

The only variable that changes is n–the numerator of that equation stays the same. So, all we need to do is account for the square root of 4n, which is 2n, so you can divide by 2.

When your sample size increases by a factor of X you divide the SD by a factor of sqrtX

As N increases SD decreases for a sampling dist!!

Margin of error is the standard error times the critical value. This formula only gives the standard error.

so p =/= .15 in this?

p hat is 0.15 in this