Question

Consider an x distribution with standard deviation σ = 32.
(a) If specifications for a research project require the standard error of the corresponding x distribution to be 4, how large does the sample size need to be?
n =  

(b) If specifications for a research project require the standard error of the corresponding x distribution to be 1, how large does the sample size need to be?
n =

Answer 1

Consider an x distribution with standard deviation σ = 32.
(a) If specifications for a research project require the standard error of the corresponding xdistribution to be 4, how large does the sample size need to be?

We have

Standard error = σ/sqrt(n)

Sqrt(n) = σ/standard error

n = (σ/standard error)^2

n =  (32/4)^2

n = 8^2

n = 64

Required sample size = 64

(b) If specifications for a research project require the standard error of the corresponding xdistribution to be 1, how large does the sample size need to be?
We have

Standard error = σ/sqrt(n)

Sqrt(n) = σ/standard error

n = (σ/standard error)^2

n =  (32/1)^2

n = 32^2

n = 1024

Required sample size = 1024