Statistics Problem Need Help!

Question

What sample size is required in order that the standard deviation of X(with bar) be:

 

A. 1/4 of the population standard deviation?

 

B. 1/7 of the population standard deviation?

 

C. 12% of the population standard deviation?

Answer 1

The sample standard deviation s and the population standard deviation σ are related by the equation 

 

s = σ/√n 

 

where n is the sample size.  

 

So √n = σ/s 

 

If you want s = (1/4)*σ then σ = 4*s so √n = 4*s/s = 4  ==>  n = 16 

 

If you want s = (1/7)*σ then σ = 7*s so √n = 7  ==>  n = 49

 

If you want s = 0.12*σ then √n = (1/0.12) = 8.3333  ==>  n = 69.44  

n = 69 is the closest integer but the value of s will be 1/√69 = 0.1204*σ  

If you want s to be less than 12% of σ then choose n = 70 with s = 1/√70 = 0.1195*σ