An apartment has 25 units The number of individuals living i

An apartment has 25 units. The number of individuals living in each unit is presented below:

2 3 4 5 1

2 5 2 2 4

3 2 3 4 3

1 1 1 3 5

4 3 3 5 2

Using the first and fourth columns as a sample, what would the sampling error be?

Solution

The difference between the means of two samples, A and B, both randomly drawn from the same normally distributed source population, belongs to a normally distributed sampling distribution whose overall mean is equal to zero and whose standard deviation (\"standard error\") is equal to square.root[(sd2/na) + (sd2/nb)]
where

sd2 = the variance of the source population (i.e., the square of the standard deviation);
na = the size of sample A; and
nb = the size of sample B.
  
Sample A.
Mean = 2.4
S.D a = 1.1402
n1 = 5

Sample B.
Mean = 3.8
S.D a= 1.3038
n1 = 5

S.E = Sqrt( 1.30005604/5+1.69989444/5) = Sqrt( 0.6) = 0.7745