Suppose a random sample of size 50 is selected from a population with μ = 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.
b. The population size is N = 50,000.
c. The population size is N = 5000.
d. The population size is N = 500.

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AFOKE88 AFOKE88 · Answer 1 · 2021-06-14T04:52:55+02:00

In the question, it's σ = 10 and not μ = 10.

Answer:

A) σ_x = 1.4142

B) σ_x = 1.4135

C) σ_x = 1.4073

D) σ_x = 1.343

Step-by-step explanation:

We are given;

n = 50

σ = 10

A) Formula for standard error of the mean for infinite size is;

σ_x = σ/√n

Thus;

σ_x = 10/√50

σ_x = 1.4142

B) When population is finite, we use correction factor and thus, we have;

σ_x = [√((N - n)/(N - 1)] × σ/√n

N = 50,000

Thus;

σ_x = [√((50000 - 50)/(50000 - 1)] × 10/√50

σ_x = 1.4135

C) N = 5000

Thus;

σ_x = [√((5000 - 50)/(5000 - 1)] × 10/√50

σ_x = 1.4073

D) N = 500

Thus;

σ_x = [√((500 - 50)/(500 - 1)] × 10/√50

σ_x = 1.343