Question

Consider an x distribution with standard deviation σ = 46.

(a) If specifications for a research project require the standard error of the corresponding x distribution to be 2, 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

Solution:

Given: x distribution with standard deviation σ = 46

Part a) We have to find sample size n such that specifications for a research project require the standard error of the corresponding x distribution to be 2.

That is we have : SE = 2

Standard Error SE is given by formula:

Squaring on both sides, we get:

Thus required sample size n is: n = 529

Part b) find sample size n such that specifications for a research project require the standard error of the corresponding x distribution to be 1.

That is: SE = 1

Thus

Squaring on both sides, we get:

Thus required sample size is: n = 2116