Question

Consider a target population of N = 220 units. Suppose x is to be
estimated with a simple random sample of n = 12 units. Data is given below.

Data: (43, 28, 40, 55, 39, 34, 31, 42, 46, 37, 44, 43).

If we ignore the fact that the population is finite and treat the
sampling fraction f as f = 0 recompute s(xbar) . Using the finite population result as the
reference, by what percentage does s(xbar ) change when the population is treated as infinite?

Answer 1

Population size = N = 220

Sample size = n = 12

First we need to find samle standard deviation for data that is s_x

Let's used excel:

First enter the data in excel column

then use "=STDEV(range of data)" this command to find the sample standard deviation

so we get s = 7.19638

If we ignore samplinf fraction then the formula of   is

so that  

Sampling fraction = f = 1 - (n/N) = 1 - (12/220) = 0.945455

Using the finite population result we get f * = 0.945455 * 2.077414 = 1.964102

Therefore % changes = { (new value - old value ) / old value } * 100

% changes = {( 1.964102 - 2.077414) / 2.077414 }*100 = -5.45 %

That is the reduction in is about 5.45% when we consider the finite population