Question

Suppose a random sample of size 60 is selected from a population with

σ = 10.

Find the value of the standard error of the mean in each of the following cases. (Use the finite population correction factor if appropriate. Round your answers to two decimal places.)

(a)

The population size is infinite.

Correct: Your answer is correct.

(b)

The population size is

N = 60,000.

Correct: Your answer is correct.

(c)

The population size is

N = 6,000.

Incorrect: Your answer is incorrect.

(d)

The population size is

N = 600.

Incorrect: Your answer is incorrect.

Answer 1

Solution:

n = 60 (sample size)

= 10 (Population standard deviation)

a) Population size N is infinite

So , population correction factor is not necessary.

Standard Error = /n = 10/60 = 1.29

Answer : 1.29

b) N = 60000

n/N = 60/60000 = 0.001 not greater than 0.05

So , population correction factor is not necessary.

Standard Error = /n = 10/60 = 1.29

Answer : 1.29

c) N = 6000

n/N = 60/6000 = 0.01 not greater than 0.05

So , population correction factor is not necessary.

Standard Error = /n = 10/60 = 1.29

Answer : 1.29

d) N = 600

n/N = 60/600 = 0.1 greater than 0.05

So , population correction factor is necessary.

PFC =   

=  

   = 0.94947485705

Standard Error = [/n ] * PFC = [10/60 ]*  0.94947485705= 1.23

Answer : 1.23