Question

Suppose a random sample of size 60 is selected from a population withσ = 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 isN = 60,000.Correct: Your answer is correct.(c)The population size isN = 6,000.Incorrect: Your answer is incorrect.(d)The population size isN = 600.Incorrect: Your answer is incorrect.

Answer 1

Answer:

a) 1.29

b) 1.29

c) 1.28

d) 1.23

Step-by-step explanation:

We are given the following in the question:

Sample size, n = 60

Population standard Deviation = 10

a) Standard error with infinite population

$\text{Standard error} = \displaystyle\frac{\sigma}{\sqrt{n}} = \frac{10}{\sqrt{60}} = 1.29$

For finite population with size N,

$\text{Standard error} = \sqrt{\displaystyle\frac{N-n}{N-1}}\times \displaystyle\frac{\sigma}{\sqrt{n}}$

b) N = 60,000

$\text{Standard error} = \sqrt{\displaystyle\frac{60000-50}{60000-1}}\times \displaystyle\frac{10}{\sqrt{60}} = 1.29$

c) N = 6,000

$\text{Standard error} = \sqrt{\displaystyle\frac{6000-50}{6000-1}}\times \displaystyle\frac{10}{\sqrt{60}} = 1.28$

d) N = 600

$\text{Standard error} = \sqrt{\displaystyle\frac{600-50}{600-1}}\times \displaystyle\frac{10}{\sqrt{60}} = 1.23$