I have a sample of 50 trees and this sample gives me a stand

I have a sample of 50 trees and this sample gives me a standard error of 15 cm for mean tree height. If I double the replication, by how much do I reduce the error in mean tree height? Hint: use the equation for the standard error to deduce the standard deviation

Question 1 options:

By about a third

By about 10%

By about 10 times

By about half

Solution

standard error =s/vn =15

--> s/sqrt(50) = 15

--> s= 15*sqrt(50) =106.066

So double the replication:

standard error =s/vn =106.066/sqrt(50*2) =10.6066

1-10.6066/15 =0.2928933

Answer: By about a third